The Summer School in Mathematics 2022 (Institut Fourier, Grenoble) will take place from June 13th to July 1st, 2022 and will be dedicated to Cohomology, Geometry and Explicit number theory (COGENT).

It will be a hybrid event with both in-person and online participation.

The goal of this school is to introduce young mathematicians to some recent developments in the field of cohomology of groups, with a focus on arithmetic groups, from geometrical, topological and computational aspects with applications to number theory. We also want to promote greater interaction among researchers and PhD students,​ and strengthen the COGENT network through new collaborations.

The first two weeks are dedicated to mini-courses and mini-workshops around some computational tools and new computational techniques, as well as short term team projects.

The third week will be devoted to a workshop on COGENT featuring both young researchers and leading specialists.

There will also be an "Illustrating mathematics'' event with an art exhibitions showcasing artistic visuals related to the geometries of arithmetic groups.

website: https://if-summer2022.sciencesconf.org/

We have partial funding for the accommodation of participants. Registration is mandatory for both on-site and online participation (including for the third week workshop). (see https://if-summer2022.sciencesconf.org/resource/page/id/1),

Registration for on-site participation will close on May 16, 2022. Registration for online participation is open and will close on June 6th, 2022.

We acknowledge the support of the Institut Fourier, of the CNRS, of the LabEx Persyval, of the GDR JC2A, of U. Grenoble Alpes and Grenoble-INP, of Grenoble-Alpes Métropole and of the MSTII Doctoral School for the organisation of this event.

Looking forward to seeing you in Grenoble.

The organizers: B. Eick (TU Braunschweig), Ph. Elbaz-Vincent (U.Grenoble Alpes), G. Ellis (NUI Galway), P. Gunnells (U. Massachusetts-Amherst), H. Sengun (U. Sheffield)

Contact organizer: [email protected] Contact staff: Géraldine Touvier ([email protected])

The conference is devoted to equidistribution results for algebraic numbers, and more generally, points of small height in various number theoretic settings, with emphasis on applications to arithmetic dynamics. Eleven one-hour plenary talks and several sessions of 25-minute contributed talks will be scheduled. We will also have problem sessions and discussion groups with the goal of compiling a list of problems and setting possible approaches to their solutions. Graduate students and recent PhDs, particularly women and underrepresented minorities, are especially encouraged to participate. Two introductory mini-courses, on the uniform distribution of algebraic numbers and on arithmetic dynamics, will be given at the conference.

The relationship between L-functions, automorphic forms and Galois representations is a central theme in Number Theory. Some of the most intriguing aspects of this relationship are the conjectural links between analytic properties of L-functions and arithmetic invariants of varieties over number fields. These links, known as Bloch–Kato conjectures, can be seen as a vast generalization of the class number formula for Dedekind zeta-functions and the conjecture of Birchand Swinnerton-Dyer for elliptic curves. The only known way to attack these conjectures is to relate the underlying geometric objects to automorphic forms using the Taylor–Wiles method and to study special values of L-functions via Iwasawa theory. The latter approach requires an extensive development of the theory of p-adic L-functions. From this point of view, the p-adic analogs of the Bloch–Kato conjecture include the p-adic Beilinson Conjectures, formulated by Perrin-Riou, and the Main Conjectures of Iwasawa theory. The last two decades have seen spectacular progress in the use of p-adic methods to solve new instances of the Bloch-Kato Conjectures. The method of Euler systems, initially invented by Kolyvagin and Kato in the context of modular forms, was partially extended to some new situations (Rankin–Selberg L-functions, triple products, symplectic groups) and applied to Gross-Stark conjectures. The generalization of the Ribet–Wiles approach to some unitary groups lead to the proof of the Greenberg Main Conjecture for a large class of modular forms. The theory of Selmer complexes generalized and simplified algebraic aspects of the theory, and found impressive appli-cations to the Parity Conjecture. Classical constructions of p-adic L-functions were extended to algebraic groups of higher ranks. Also the realm of interaction between automorphic forms and Galois representations is in full bloom, and recently established R = T theorems have led to proofs of generalizations of Serre’s Modularity Conjecture and the Sato-Tate Conjecture. The aim of the conference is to bring together leading experts and emerging scientists, to report on the latest developments, to foster scientific exchanges, to initiate new interaction and collaboration, and thereby contribute to the scientific advancement of the field.

The ICM 2022 Satellite Conference "Hochschild (co)homology and derived categories" will be held at St Petersburg Department of Steklov Mathematical Institute from 20 to 24 June 2022.

The event will focus on presenting the latest developments in topics of homological and homotopical algebra related to Hochschild (co)homology.

Speakers will include:

Benjamin Briggs • University of Utah

Claude Cibils • Université de Montpellier

Karin Erdmann • Oxford University

Vincent Gélinas • Desjardins

Estanislao Herscovich • Université Grenoble Alpes

Srikanth Iyengar • University of Utah

Janina Letz • Universität Bielefeld

Markus Linckelmann • City University

Ayelet Lindenstrauss • Indiana University Bloomington

Maria Julia Redondo • Universidad Nacional del Sur

Travis Schedler • Imperial College London

Sibylle Schroll • Universität zu Köln

Greg Stevenson • University of Glasgow

Mariano Suárez-Álvarez • Universidad de Buenos Aires

Rachel Taillefer • Université Clermont Auvergne

Zhengfang Wang • Universität Stuttgart

Guodong Zhou • East China Normal University

Alexandra Zvonareva • Universität Stuttgart

For more details and to register see the webpage

https://indico.eimi.ru/event/315/.

Note that visa-free entry to the Russian Federation from 01.03.2022 to 01.09.2022 will be available to registered participants of the Congress, including those who plan to participate in satellite events.

To avail of that, one has to register at the Congress website and pay the registration fee. Please check the ICM webpage at https://icm2022.org/visa-free-entry for further details.

We plan to provide some financial support for participants from developing countries and young participants without access to travel funding.

Deadlines:

Proposals of contributed talks: March 15, 2022

Requests for financial support: March 15, 2022

General registration: April 15, 2022

Best wishes,

Organising Committee: Vladimir Dotsenko (Université de Strasbourg), Bernhard Keller (Université de Paris), Andrea Solotar (Universidad de Buenos Aires), Yury Volkov (St Petersburg University)

Scientific Committee: Luchezar Avramov (University of Nebraska - Lincoln), Yang Han (Chinese Academy of Sciences), Henning Krause (Universität Bielefeld), Wendy Lowen (Universiteit Antwerpen), Birgit Richter (Universität Hamburg)

The workshop will be devoted to the study of surfaces with special metrics with singularities of conical type.

In particular it will focus on the case of spherical metrics, namely Riemannian metrics of curvature 1. Such metrics have been studied from many points of view, using tools coming from synthetic geometry, complex analysis and partial differential equations.

The aim of the meeting is to bring together people with different backgrounds to discuss recent developments, techniques and open questions in the areas of spherical surfaces with conical points, projective structures with singularities and their monodromy, solutions of the singular Liouville equation, polyhedral spherical surfaces, polygonal linkages.

RNT-3 will be a remote collaborative research experience supported, in part, by the American Institute for Mathematics for the weeks of June 20 - July 1. The goal is for participants to learn new math, get to know colleagues, and have a joyful, affirming research experience. Workshop meetings will be planned around our busy schedules so that we can work on exciting research while also keeping up with our teaching and family responsibilities. Team leaders have planned projects for participants to work on during the workshop. You can read more about the projects here.

To ensure that all participants can share in this joyful research experience, we ask that all who apply to participate be committed to equity and justice. We will also make time to imagine a different way to do math: How could research seminars, postdoc positions, and graduate school be transformed to be comfortable to everyone? We will have a code of conduct for the workshop, which you can read here.

To participate in our workshop, please apply by the end of the day on May 15, 2022 The application is here.

RNT aims to foster diversity; we particularly encourage applications from historically underrepresented people in mathematics (including Black and Indigenous people, people of color, women, LGBTQ+ members of the community, and people with disabilities), scholars at undergraduate institutions, and in general scholars at all stages of their career who believe they would benefit from this experience. Please share this announcement with any groups, students, post docs, or scholars who might be interested in participating in this workshop. If you have questions, please email the organizers at: [email protected]

On April 6, 1972 a young graduate student named Hugh Montgomery and the world-renowned mathematical physicist Freeman Dyson had a conversation in the tearoom at the Institute for Advanced Study which led to a fusion of two disparate fields and an intellectual revolution that is stronger than ever today. Montgomery and Dyson discovered that the zeros of the Riemann zeta-function, important for understanding prime numbers, seem to obey the same distribution patterns as the eigenvalues of large random unitary (or hermitian) matrices, which had been extensively studied by physicists, especially to model the interactions within large atomic nuclei. This stunning connection has held up to extensive numerical and theoretical tests over the intervening years and has been extended to give random matrix models for the low lying zeros of families of L-functions and for the moments and distribution of values of the L-functions in these families and to analogous families over function fields. This conference will bring together 130 mathematical scientists to a meeting that will highlight the progress and the state of the art of results at the nexus of these two fields and will underline the questions most pertinent for further research.

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

Join us for a five-day workshop hosted by Western Washington University. Mornings will be dedicated to talks, and in the afternoons, participants will work on open problems related to 4-manifold trisections in small groups. The deadline to apply for support is April 22, 2022.

The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra. On the other hand, many problems in numerical linear algebra lead to linear, nonlinear or semidefinite optimization problems. The purpose of the conference is to bring together researchers from both communities and to find and communicate points and topics of common interest. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM). Conference topics include any subject that could be of interest to both communities, such as: • Direct and iterative methods for large sparse linear systems. • Eigenvalue computation and optimization. • Large-scale nonlinear and semidefinite programming. • Effect of round-off errors, stopping criteria, embedded iterative procedures. • Optimization issues for matrix polynomials • Fast matrix computations. • Compressed/sparse sensing • PDE-constrained optimization • Distributed computing and optimization • Applications and real time optimization Invited Speakers Invited Speakers to be confirmed shortly. Registration Registration is currently open at https://my.ima.org.uk/ If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in. Call for Papers and Mini-Symposiums Mini-symposium proposals and contributed talks are invited on all aspects of numerical linear algebra and optimization. Mini-symposium proposals should be submitted to [email protected] by 31 January 2022. A mini-symposium consists of up to four speakers. For emerging topics the mini-symposium can be extended to at most two sessions on a single topic (maximum eight speakers). Organisers will be advised of acceptance by 14 February 2022. Contributed talks and mini-symposia talks will be accepted on the basis of a one page extended abstract which should be submitted by 28 February 2020 online at http://online.ima.org.uk/ or by e-mail to [email protected] Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference. Key deadlines Mini-symposia proposals: 31 January 2022 Notification of acceptance of mini-symposia: 14 February 2022 Abstract submission: 28 February 2022 Notification of acceptance of abstracts: 31 March 2022 Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference.

Early Bird Conference Fees IMA/SIAM Member - £395.00 Non IMA/SIAM Member - £450.00 IMA/SIAM Student - £215.00 Non IMA/SIAM Student - £225.00 Conference Fees will increase by £20 on 22 May 2022 Day Delegate rate: A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at [email protected]

Accommodation The IMA have booked accommodation at Edgbaston Park Hotel on hold for delegates on a first-come, first-serve basis. The room is £90 Single occupancy, B&B which will be available to book until 16/05/2022. If you are interested in booking at this rate, please contact the Conferences Department for the booking code.

Organising Committee Michal Kocvara, University of Birmingham (co-chair) Daniel Loghin, University of Birmingham (co-chair) Coralia Cartis, University of Oxford Nick Gould, Rutherford Appleton Laboratory Philip Knight, University of Strathclyde Jennifer Scott, Rutherford Appleton Laboratory Valeria Simoncini, University of Bologna Contact information For general conference queries please contact the Conferences Department, Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK. E-mail: [email protected] Tel: +44 (0) 1702 354 020

The IMA is pleased to announce the Seventh Biennial IMA Conference on Numerical Linear Algebra and Optimization. The success of modern codes for large-scale optimization is heavily dependent on the use of effective tools of numerical linear algebra. On the other hand, many problems in numerical linear algebra lead to linear, nonlinear or semidefinite optimization problems. The purpose of the conference is to bring together researchers from both communities and to find and communicate points and topics of common interest. This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM). Conference topics include any subject that could be of interest to both communities, such as: • Direct and iterative methods for large sparse linear systems. • Eigenvalue computation and optimization. • Large-scale nonlinear and semidefinite programming. • Effect of round-off errors, stopping criteria, embedded iterative procedures. • Optimization issues for matrix polynomials • Fast matrix computations. • Compressed/sparse sensing • PDE-constrained optimization • Distributed computing and optimization • Applications and real time optimization Invited Speakers: Invited Speakers to be confirmed shortly.

Registration: Registration is currently open at https://my.ima.org.uk/ If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.

Call for Papers and Mini-Symposiums: Mini-symposium proposals and contributed talks are invited on all aspects of numerical linear algebra and optimization. Mini-symposium proposals should be submitted to [email protected] by 31 January 2022. A mini-symposium consists of up to four speakers. For emerging topics the mini-symposium can be extended to at most two sessions on a single topic (maximum eight speakers). Organisers will be advised of acceptance by 14 February 2022. Contributed talks and mini-symposia talks will be accepted on the basis of a one page extended abstract which should be submitted by 28 February 2020 online at http://online.ima.org.uk/ or by e-mail to [email protected] . Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference. Key deadlines: Mini-symposia proposals: 31 January 2022 Notification of acceptance of mini-symposia: 14 February 2022 Abstract submission: 28 February 2022 Notification of acceptance of abstracts: 31 March 2022

Authors will be advised of acceptance by 31 March 2022. A book of abstracts will be made available to delegates at the conference. Early Bird Conference Fees: IMA/SIAM Member - £395.00 Non IMA/SIAM Member - £450.00 IMA/SIAM Student - £215.00 Non IMA/SIAM Student - £225.00 Conference Fees will increase by £20 on 22 May 2022 Day Delegate rate: A Day Delegate rate is also available for this Conference if you would like to attend one of the scheduled Conference days. If you would like to find out more information about our Day Delegate rate, please contact us at [email protected] Accommodation: The IMA have booked accommodation at Edgbaston Park Hotel on hold for delegates on a first-come, first-serve basis. The room is £90 Single occupancy, B&B which will be available to book until 16/05/2022. If you are interested in booking at this rate, please contact the Conferences Department for the booking code. Organising Committee: Michal Kocvara, University of Birmingham (co-chair) Daniel Loghin, University of Birmingham (co-chair) Coralia Cartis, University of Oxford Nick Gould, Rutherford Appleton Laboratory Philip Knight, University of Strathclyde Jennifer Scott, Rutherford Appleton Laboratory Valeria Simoncini, University of Bologna

Contact information: For general conference queries please contact the Conferences Department, Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK. E-mail: [email protected]

The second Azat Miftakhov Days will take place on Tuesday and Wednesday July 5-6, 2022, in solidarity with Azat Miftakhov, a mathematics graduate student from the Moscow State University who has been arbitrarily detained by Russian state authorities since February 2019.

• Tuesday July 5, 2022 from 4pm to 7pm Central European Summer Time (UTC+2) – online.

On the first day, we will honor the new generation of Russian mathematicians committed to human rights. The speakers are Ilya Dumanski (MIT), Alexander Petrov (Harvard) and Slava Rychkov (IHES). Their mathematical lectures will be broadcast live on Zoom and youtube.

• Wednesday July 6, 2022 from 5pm to 7pm Central European Summer Time (UTC+2) – hybrid.

On the second day, we will co-organize with Memorial Human Rights Center a panel to assess the human rights situation in Russia through the cases of persecuted academics. The panel will be hybrid, online and in person at the École normale supérieure in Paris, open to academics, human rights organizations and journalists.

Registration is mandatory both for participation online or in person. The registration form is available here (https://tinyurl.com/4wcwbrb6).

Spec(Q¯¯¯¯) is the first conference to celebrate and promote research advances of LGBT2Q mathematicians specialising in algebraic geometry, arithmetic geometry, commutative algebra, and number theory. This conference capitalises on recent thematic program successes in algebraic geometry at Fields, the Thematic Program on Combinatorial Algebraic Geometry (July 1 - December 31, 2016) and the Thematic Program on Homological Algebra of Mirror Symmetry (July 1 - December 31, 2019). Spec(Q¯¯¯¯) will create an empowering and engaging environment which provides LGBT2Q visibility in algebraic geometry, will support junior LGBT2Q academics, and will crystallise new collaborative networks for participants. Algebraic geometry, classically, is the study of the geometry of solutions of polynomial equations; through modern advances it has become an intersectional mathematical field, drawing from various aspects of algebra, number theory, geometry, combinatorics and even mathematical physics. This conference aims to highlight strong mathematical research in a wide array of algebraic geometry, broadly defined. The conference will feature some plenary talks by world-leading researchers from a range of areas of algebraic geometry. To facilitate new connections across the various threads of algebraic geometry, plenary talks at Spec(Q¯¯¯¯) will be aimed a general algebro-geometric audience.

This activity will bring together mathematicians spanning all academic ranks to create ideal networking and mentorship for LGBT2Q academics while disseminating key achievements of trans and queer algebraic geometers. Queer and trans academics often have a diffcult experience developing key collaborations and networks of trusted colleagues. Each research connection, grant, and application involves a conscious decision of how much of one’s queer/trans identity to disclose. This conference provides a safe space to develop ones network while removing these barriers. In such spaces, one can discuss mathematics with new colleagues while unbridled with many societal challenges that they face in mathematical communities. When a mathematician feels free to be themselves in all ways, they are able to immerse themselves in creative mathematical thought.

The official ICM 2022 has been reorganised as an online event. We will host some of the talks real life in Copenhagen, and attempt to salvage, on a smaller scale, some of the usual spirit of an ICM. The focus of the event in Copenhagen will be the Geometry and Topology sections, though it will not be restricted to those. See the webpage for more info.

Description The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. The workshop will be centered around mini-courses, both on classical fixed-point theory and on modern techniques such as duality theory, spectra, and trace methods in algebraic K-theory.

The intended audience for this summer school should be familiar with the material in Hatcher (except the appendices). This reflects our goal that the school be accessible to second and third year students with an interest in algebraic topology. The school will be structured around a few mini-courses, which will run in an active-learning style.

The target audience is graduate students or other early career people in fields related to Floer Homotopy Theory, very broadly construed. Please tell anyone you know who might be interested.

The application to attend can also be found on the event page. The deadline to apply is 4 February 2022. Housing will be provided for at least the first 50 accepted applicants.

There is a registration fee (to be paid later) to discourage spurious registrations, but this can be waived if it is an obstacle to attendance.

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Speakers and Courses:

 Mohammed Abouzaid, Columbia University: Floer Homotopy
 Omar Antolín, UNAM: Introduction to Ring Spectra
 Nate Bottman, Max Planck: Floer Homology Fundamentals
 Catherine Cannizzo, SCGP: Floer Homology Fundamentals
 Jeff Hicks, University of Edinburgh: Applications
 Cary Malkiewich, Binghamton University: Spectra and Smash Products
 Katherine Poirier, New York City College of Technology: String Topology 
 Hiro Lee Tanaka, Texas State University: Operads

School Structure:

The summer school will consist of lecture courses with problem sessions; seminars on recent developments; and two panel discussions about professional development. The lecture courses will be:

Week 1

Fundamentals of Floer homology (9 lectures)

Introduction to ring spectra (3 lectures)

String topology (3 lectures)

Week 2

Spectra and smash products (4 lectures) Operads (4 lectures)

Applications of Floer homology (3 lectures)

Floer homotopy theory (4 lectures)

Most days, an hour and a half will be set aside for problem sessions. There will also be two seminars on recent developments and one panel discussion on professional development each week.

new description:

It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.

Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.

The summer school will attempt to bring these exciting new directions together and explore their interactions.

The conference aims to bring together researchers in optimal control, dynamic games, and nonlinear dynamical systems, as well as scientists in all application areas. The workshop topics will include the theory and numerical methods of optimal control of ordinary and distributed systems, differential games, related topics in optimization theory and dynamical systems theory, and a broad spectrum of applications involving dynamic models in economics (including population, health and environmental economics), demography, biology, social sciences, engineering, etc.

CALL FOR PAPERS The study of the relationship between music and mathematics has a thousand-year-long history which predates Pythagoras. Mathematics and music share a common basis of language and creativity. From the theory of tuning systems and temperament to physical acoustics, from harmonic analysis to spectrograms, from the structures of rhythms and pulses to the continuous stretching of the laws of harmony and the exploration of the musical forms carried out by contemporary composers, all elements of music lead to an immediate connection to mathematics. Established and recent research has witnessed the use of set theory to describe how musical objects are related and organised, the use of group theory in the context of transformational analysis of tonal and atonal compositions, the application of Grassmannians to the study of temperaments, and the investigation of category theory, topology and differential geometry to provide a basis of music theory. The Institute of Mathematics and its Applications is glad to announce the launch of the first IMA conference on "Mathematics in Music", to take place on 13-15 July 2022 at the Royal College of Music, London. The conference focusses onto the exploration of the connections between mathematics and music, in particular current developments of music theory, music performance, music perception and music technology based on or inspired by mathematical applications and concepts, including (but not limited to) category theory, group theory, topology, differential geometry, combinatorics, analysis, acoustic theory, as well as artificial intelligence, deep learning, language processing and coding. The conference is aimed at mathematical researchers working at the frontier between mathematics or computation with music theory, musicology, music performance, sound engineering and composition, as well as at musicologists or computational musicologists, performers and composers using quantitative tools and formal methods from mathematics in their investigation and professional practice of music. Invited Speakers: Prof Emily Howard, Royal Northern College of Music Prof Guerino Mazzola, University of Minnesota Prof Geraint Wiggins, Vrije Universiteit Brussel & Queen Mary University of London Moreno Andreatta, CNRS Director of Research at IRMA Call for Abstracts: Abstract Submission of 300 words by the 31 March 2022. via https://my.ima.org.uk. Note: If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in

Registration: Registration for this Conference is currently open. https://my.ima.org.uk/services.php?section=events

If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in.

Conference Fees: IMA/RCM Member – £150 Non-Member – £300 Student IMA/RCM Student Member – £100 Non-Member Student - £120

Important Dates: Call for papers deadline – 31 March 2022 Papers acceptance notification – 15 April 2022 Scores selection notification – 1 April 2022 Final registration date – 1 July 2022 Conference Dates – 13-15 July 2022

Organising Committee: Matteo Sommacal, Northumbria University Michelle Phillips, Royal Northern College of Music Dimitri Scarlato, Royal College of Music Rob Sturman, Leeds University

Further information: E-mail: [email protected]
Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK. In cooperation with the Royal College of Music

The workshop is online from July 18 to July 20th, 2022.

The algebraic topology and algebraic geometry in China are still developing, especially in the mid-south area. We hope we can help developing the math areas as much as we can. We plan to organize a 1-2 days workshop every quarter and a 3-5 days worshop every year in these areas. We also have online joint undergraduate seminars in algebraic topology and algebraic geometry.

If you are interested in giving a talk in one of the MSATG workshops, or you would like to give us some comments, feel free to contact us.

Huan, Zhen (Huazhong University of Science and Technology), [email protected]

Sun, Hao (South China University of Technology), [email protected]

International conference on recent advances in p-adic L-functions and p-adic families of automorphic forms. Preceded by a graduate workshop on the same topics.

Organizers:

• Emeric Gioan, LIRMM, France
• Johann A. Makowsky, Israel Institute of Technology- IIT, Israel
• James Oxley, Louisiana State University, USA

The Journal of Number Theory will host a number theory conference every two years to publicize recent advances in the field. The JNT is sponsoring the David Goss Prize of 10K USD to be awarded every two years at the JNT Biennial to a young researcher in number theory. Proceedings of the JNT Biennial conferences will appear in a special volume of JNT.

The Young Topologists Meeting (YTM) is an annual event that has previously been organised by the EPFL (Switzerland), the University of Copenhagen (Denmark), and jointly by Stockholm University and the Royal Institute of Technology (Sweden). The YTM 2022 it will take place on July 18-22, 2022 in Copenhagen. This yearly meeting is an opportunity for young researchers in topology to meet each other and share their work. In addition to short talks by the participants, the program for the meeting will include lectures by Andrew J. Blumberg (Columbia University), Natàlia Castellana Vila (Universitat Autònoma de Barcelona), and Robert Ghrist (University of Pennsylvania).

The conference mainly focuses on topics in pure and applied mathematics, related to the research areas mainly, Topology, Analysis and Functional Analysis, Sequences, Series, Summability, Fixed Point Theory, Differential Geometry, Algebra, Computer Science and Technology, Applied Statistics, Mathematical Methods in Physics.

The Graduate Instructional Workshop runs from July 24 to July 30 and consists of mini-courses on recent developments in the algebraic theory of automorphic forms, L-functions, and related topics. This workshop aims to help prepare students to be successful researchers by introducing key research techniques and results. For the list of mini-courses and additional details, see https://sites.google.com/view/automorphic2021/graduate-instructional-workshop

The purpose of the conference is to bring together people from all branches of mathematics and science with interests in recurrence sequences, their applications and generalizations, and other special number sequences. For the conference proceedings, manuscripts that include new, unpublished results (or new proofs of known theorems) will be considered.

The Collaborative Research Workshop runs from July 31 to August 6 and facilitates new research collaborations on algebraic aspects of automorphic forms, L-functions, and related topics, while also flipping the gender imbalance in this area. For project groups and details, see https://sites.google.com/view/automorphic2021/collaborative-research-workshop/project-groups

The summer school will feature mini-courses by Joshua Greene, Jen Hom, Francesco Lin, John Pardon (to be confirmed) and Thomas Walpuski, covering topics in low-dimensional topology, Floer homology, and gauge theory. The school will be followed by a research conference the week after. The DEADLINE for applications is FEBRUARY 28, 2022. The application page is linked to from the conference webpage. Applicants are expected to provide a recommendation letter from their PhD advisor.

Automorphic forms are present in almost every area of modern number theory. In recent decades there has been a starburst of activity and progress in this broad area, leading to many new and exciting directions, applications, and connections with other areas. This is a rapidly expanding area, with numerous approaches, tools, and interconnections, as well as connections to other areas of mathematics. The Building Bridges research school offers training to graduate students and early career researchers in the areas of automorphic forms and related topics that continue to be the foci of exciting and influential research activity. The five-day workshop immediately following the summer school aims to foster and strengthen a long-lasting, friendly and supportive exchange between automorphic forms researchers in the EU and the US, and to integrate the summer school students into this community. The organizers have obtained funding to subsidize the costs of successful applicants to the summer school. By popular demand from previous research school and workshop participants, BB5 will take place in Sarajevo, a beautiful city with a friendly, multicultural atmosphere, and low costs of accommodation, food, and transportation.

The aim of the school is to give an overview of established results and current research on elliptic curves by covering the whole spectrum of techniques developed so far.

There will be 6 courses of 3 hours each plus exercises sessions.

• Course 1 : Analytic Methods - Alina Cojocaru
• Course 2 : Arithmetic Statistics - Jennifer Park
• Course 3 : Modularity-based Methods - Chao Li
• Course 4 : Points and Heights - Joseph Silverman
• Course 5 : Selmer Groups - Christian Wuthrich
• Course 6 : Torsion Points - Jan Vonk

The ANTS meetings, held biannually since 1994, are the premier international forum for the presentation of new research in computational number theory and its applications. They are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.

The conference will cover several areas of current research, including low-dimensional topology, gauge theory, and Floer homology in all its flavors. It is partly intended to celebrate the mathematical contributions of Tomasz Mrowka. The conference will be preceded by a summer school for graduate students (the week before). The list of speakers is on the event webpage. That webpage also contains a link to the application page. The DEADLINE for participants to apply is FEBRUARY 28, 2022.

This event consists of two parts: a 2-day workshop for early career participants, followed by a 5-day conference for participants at all career stages. The topic is the Langlands program, including local and global, geometric and p-adic aspects. The principal aim of the two events is to help (re)build research networks that have been affected by the pandemic. For more details see https://www.hcm.uni-bonn.de/events/eventpages/2022/clap/

The conference will also include a number of contributed talks. If you are interested in giving a contributed talk, please submit the title and abstract of your talk as part of your application form.

The deadline for applications to participate in the workshop/conference is January 31, 2022 (CET).

Aim: To discuss categorical invariants and how to handle them with abstract methods. For 5 days, we are going to exchange ideas and hunt for new lines of thought.
Target group: Postdocs and PhD students.
Keynotes: Keynotes on the topic will be delivered by Dimitri Zvonkine, Junwu Tu and Fabian Haiden.
Setting: The event takes place in Jasper's backyard in the outskirts of Berlin. Facilities and meals are provided. The calm surroundings and liberal atmosphere enable a total focus on mathematical discussion.
US residents: US residents are more than welcome. The workshop includes an excursion in Berlin.
Register now! You find more information on the website.

The year 2022 marks the centenary of Mordell's 1922 paper "On the Rational Solutions of the Indeterminate Equations of the Third and Fourth Degrees", in which Mordell both established the foundational result in the arithmetic of elliptic curves (finite generation of rational points), and proposed what later became Mordell's Conjecture (and subsequently Faltings' Theorem).

In recognition of this anniversary, this conference will be a celebration of all aspects of the arithmetic of elliptic curves.

The summer school aims to explore exciting applications of modular forms in different areas of Mathematics and provide a friendly and helpful environment to discuss and explore these concepts.

The summer school will consist of three courses given by Eugenia Rosu, Sven Möller, and a third researcher who will be confirmed later. Each course will consist of three lectures of 60-90minutes. There will be breaks in between to meet the other participants and discuss the content of the courses. More details will be shared closer to the date of the summer school.

The participants are expected to know the basics definition of (elliptic) modular forms.

Workshop for researchers from different backgrounds who are interested in modular forms in number theory and other mathematical disciplines organized by Claudia Alfes-Neumann, Michael Mertens and Markus Schwagenscheidt.

This is a workshop that aims to support new collaborations for women in number theory. Prior to the conference, the project leaders will design projects and provide background reading and references for their groups. Each participant will be assigned to a working group according to her research interests. During the workshop there will be some talks and career-development activities, but there will also be ample time dedicated to working in the working groups.

The theory of automorphic forms is a dynamically expanding part of number theory with an increasing number of connections and applications to other branches of mathematics as well as physics. Research is driven by long standing conjectures and unexpected breakthroughs.

The purpose of this special semester is to bring together established researchers as well as those just starting their careers or studies. We would like to provide a rich and stimulating environment for interactions. There will be ample opportunity for the participants to present classical results and new developments. It is hoped that visits within this program will lead to further collaborations and progress.

The workshop aims at bringing together experts and young researchers working in the field of anisotropic isoperimetric problems, with a particular focus on the following subjects:

(A) Isoperimetric problems with density;

(B) Crystals and periodic structures;

(C) Gamow liquid drop model;

(D) Isoperimetric problems in geometric structures;

(E) Spectral problems.

Depending on the evolution of the covid-19 pandemic, the number of allowed participants will change. Further information and a registration form will follow soon.

The two-day conference Connections Workshop: Floer Homotopy Theory will run September 8th and 9th at the Mathematical Sciences Research Institute (MSRI). This workshop will feature talks by experts in Floer theory (and its applications to low-dimensional topology) and homotopy theory. It will include two expository lectures aimed at graduate students and other researchers who are new to the field, as well as a five research talks, given by the following speakers.

Expository Talks

• Jennifer Hom, Georgia Institute of Technology
• Mona Merling, University of Pennsylvania

Research Talks

• Po Hu, Wayne State University
• Xin Jin, Boston College
• Inbar Klang, Columbia University
• Shira Tanny, Institute for Advanced Study
• Melissa Zhang, University of Georgia

There will also be a contributed talks session and a panel discussion focusing on professional development. This workshop will highlight contributions by women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians. The deadline for applying for funding is June 1; contributed talks will be solicited shortly thereafter.

This workshop precedes the weeklong Introductory Workshop: Floer Homotopy Theory, which may also be of interest to participants.

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

The goal of this summer school is to introduce the participants to motivic integration and some of its applications. It is mainly aimed at PhD students and Postdocs who do work in an area around algebra and/or geometry, but who have not yet had any prior contact to this motivic integration. There will be three minicoures, which will explain the necessary tools and background material, give down-to-earth motivation and examples, and which will end with some interesting applications. In addition, there will be around ten one-hour talks about current research related to motivic integration. The summer school is part of the program of the DGF-funded research training group.

Isaac Newton Institute for Mathematical Sciences, Cambridge 14 – 15 September 2022 https://ima.org.uk/19278/induction-course-for-new-lecturers-in-the-mathematical-sciences-2022/

IMANewLecturers2022

Through a community initiative supported by the Institute of Mathematics and its Applications, the Isaac Newton Institute for Mathematical Sciences and the Heads of Departments of Mathematics Sciences (HoDoMS) and endorsed by the Royal Statistical Society and the London Mathematical Society, we are delighted to announce that in September 2022 the two‐day Induction Course for lecturers new to teaching mathematics and statistics within Higher Education will once again take place. Whilst arrangements may still be subject to change due to the ongoing Covid‐19 situation and any future Government guidance, we are currently preparing for the Induction Course to be delivered as an in‐person only activity to maximise the opportunities for informal networking and discussion that have long formed a highly‐valued part of this meeting.

The Induction Course for New Lecturers in the Mathematical Sciences has been designed by the mathematics community so that it is ideally suited for anyone who is new to or has limited experience teaching mathematics or statistics within UK higher education. It will be delivered by individuals with significant experience of teaching in the mathematical sciences and will focus upon the specific details and issues that arise in mathematics and statistics teaching and learning within higher education including topics such as:

• Lecturing. • Supporting student learning. • Making teaching interactive. • Assessment, examinations and feedback. • Linking teaching & research. • Using technology to enhance teaching and learning. • Using examples and mathematical problem solving. • Teaching statistics and its applications.

Additionally, there will be significant opportunities for delegates to discuss their own ideas, challenges and experiences with the session facilitators so that individual queries can be answered.

In the past, attendance has been recognised as contributing towards some introductory institutional programmes in learning and teaching for new staff, and for the 2022 Induction Course accreditation will be provided through the Institute of Mathematics and its Applications relative to the UK Professional Standards Framework for Teaching and Supporting Learning in Higher Education.

Timing The Induction Course takes place at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge and commences mid‐morning on the 14 September, and ends late‐afternoon on the 15 September. Accommodation will be offered at the University of Cambridge on the evening of the 14 September for any delegates who attend in person, although any in‐person attendance will be dependent upon the Covid‐19 situation at the time. As such, we reserve the right to make necessary changes to arrangements in response to Government legislation and guidance.

Session Facilitators Those leading the sessions at the Induction Course are all experienced teachers of mathematics within UK higher education. They include:

• Lara Alcock (Loughborough University) • Michael Grove (University of Birmingham) • Rachel Hilliam (Open University) • Kevin Houston (University of Leeds) • Joseph Kyle (University of Birmingham) • Steve Otto (The R&A) • Chris Sangwin (The University of Edinburgh) • Louise Walker (The University of Manchester) • John Mason (Open University) • Ulrike Tillmann (Isaac Newton Institute for Mathematical Sciences)

Induction Course Costs Following generous financial support from the Isaac Newton Institute for Mathematical Sciences, the Institute of Mathematics and its Applications and the Heads of Departments of Mathematical Sciences, we are able to offer the Induction Course at the following subsidised rates:

Full residential delegate rate* (Both days including all lunches, refreshments, Course dinner and accommodation on 18 September) £299

Two‐day delegate rate (Both days including all lunches, refreshments, Course dinner but no accommodation) £240 Day delegate rate (including lunch and refreshments) £95 Induction Course dinner (as a separate purchase) £56 * Please note that accommodation is allocated on a first‐come‐first served basis.

Registration Registration is now open via https://my.ima.org.uk/.

If you are an IMA Member or you have previously registered for an IMA conference, then you are already on our database. Please “request a new password” using the email address previously used, to log in. If you are attending the conference please use the hashtag #IMANewLecturers2022 and tag the IMA on socials!

Contacts A full programme for the Induction Course will be released in July 2022, but for questions or queries about the academic content or structure of the Induction Course, please contact Michael Grove: mailto:[email protected] For general conference queries please contact: mailto:[email protected]

It is a biannual conference intended to highlight recent developments in the work of women in arithmetic geometry, and to connect promising young mathematicians with outstanding senior colleagues. Participation is open to everybody. The event is part of the newly established collaborative research center „Geometry and Arithmetic of Uniformized Structures“ between the universities of Frankfurt, Heidelberg, Darmstadt, Mainz and Münster.

The Preliminary Arizona Winter School (PAWS) is a virtual program on topics related to the upcoming AWS, with an intended audience of advanced undergraduate students and junior graduate students.

PAWS 2022 will consist of two concurrent six-week lecture series.

• Ronnie Nagloo: Introduction to model theory with applications

  Model theory is a branch of mathematical logic dealing with abstract structures, historically with connections to other areas of mathematics. The developments, over the past several decades, have allowed for a strengthening of those connections as well as new striking applications to areas such as diophantine and analytic geometry, algebraic differential equations, and combinatorics. This course will serve as an introduction to the basics of model theory, with a view towards some of the above applications.

• Padmavathi Srinivasan: Heights in Diophantine geometry

  The height of a rational number is a measure of its arithmetic complexity. For example, although the numbers 5 and 500000/100001 are close, the second is arithmetically more complex, and has a much larger height. The height of a rational number is easy to define -- it is simply the maximum of the absolute value of the numerator and the denominator when the number is expressed in lowest form. It is not immediately clear how one can extend this definition to more general algebraic numbers such as the squareroot of 2. In this series of lectures, we will develop the theory of heights of algebraic numbers, and present "Weil's height machine" for defining heights more generally for solutions to systems of polynomial equations in algebraic numbers (i.e., heights of algebraic points on varieties).

  Height functions are a key tool in proving many important finiteness theorems in Diophantine Geometry. The main property of height functions is that there are only finitely many points of bounded height and degree on any given variety. Understanding how quickly the number of points grow as the height grows for various classes of varieties is an active area of research in number theory today! As an application of the theory of heights, we will prove the Mordell--Weil theorem for elliptic curves, namely that the set of rational solutions to cubic equations such as y^2 = x^3 - 2x + 2 is finitely generated.

Registration: You can apply for the program here. The deadline to apply is July 15th, 2022.

Each lecturer will be accompanied by graduate student assistants, who will be in charge of writing weekly problem sets and facilitating weekly, hour-long problem solving and discussion meetings with groups of students. Recommended background for the program is a first course in abstract algebra.

The school will feature an online (Zulip) discussion board where students can ask questions and interact with the speakers and assistants outside of scheduled meeting times.

We will facilitate additional virtual events, some purely social to build a community, and some more structured sessions on timely and pertinent topics like "What is graduate school in Math like?", "Tips for applying to graduate school this Fall," "How do I navigate the first year of graduate school?" "How do I look for an thesis advisor?", "How to get the most out of the upcoming AWS."

We encourage undergraduate students to take their PAWS course as an independent study with a faculty member at their home institution.

• Organizers: Renee Bell, Isabel Vogt, Hang Xue, with Alina Bucur, Brandon Levin, Anthony Várilly-Alvarado, and David Zureick-Brown.
• Funded by the National Science Foundation.

A conference in honor of Bruno Kahn's 64th birthday

The workshop will focus on the interaction between homotopy theory and symplectic topology and low dimensional topology that is mediated by Floer theory. Among the topics covered are foundational questions, applications to concrete geometric questions, and the relationship with finite dimensional approaches.

The fundamental conjecture of Birch and Swinnerton-Dyer relating the Mordell–Weil ranks of elliptic curves to their L-functions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of L-functions and their leading terms to cycles and Galois cohomology groups.

The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the p-adic regulators of special cycles are directly related to the values and derivatives of L-functions, as shown in the pioneering theorem of Gross-Zagier and its p-adic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations.

The goal of this semester is to bring together researchers working on different aspects of this young but fast-developing subject, and to make progress on understanding the mysterious relations between L-functions, Euler systems, and algebraic cycles.

Number Theory concerns the study of properties of the integers, rational numbers, and other structures that share similar features. It is a central branch of mathematics with a well-known feature: it is often the case that easy-to-state problems in number theory turn out to be exceedingly difficult (e.g. Fermat’s Last Theorem), and their study leads to groundbreaking discoveries in other fields of mathematics.

A fundamental theme in number theory concerns the study of integer and rational solutions to Diophantine equations. This topic originated at least 3,700 years ago (as documented in babylonian clay tablets) and it has evolved into the highly sophisticated field of Diophantine Geometry. There are deep and fruitful interactions between Diophantine Geometry and seemingly distant fields such as representation theory, algebraic geometry, topology, complex analysis, and mathematical logic, to mention a few. In recent years, these connections have led to a large number of new results and, specially, to the partial or complete resolution of important conjectures in the field.

While the study of rational solutions of diophantine equations initiated thousands of years ago, our knowledge on this subject has dramatically improved in recent years. Especially, we have witnessed spectacular progress in aspects such as height formulas and height bounds for algebraic points, automorphic methods, unlikely intersection problems, and non-abelian and p-adic approaches to algebraic degeneracy of rational points. All these groundbreaking advances in the study of rational and algebraic points in varieties will be the central theme of the semester program “Diophantine Geometry” at MSRI. The main purpose of this program is to bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to update on recent breakthroughs, and to further advance the field by making progress on fundamental open problems and by developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field, and we strongly encourage their participation.

The Connections Workshop features presentations by both leading researchers and promising newcomers whose research has contact with the interrelated topics of algebraic cycles, L-values, and Euler systems. The goal is to present a variety of diverse results, so as to forge new connections, foster collaborative projects, and establish mentoring relationships. While emphasis will be placed on the work of women mathematicians, the workshop is open to all researchers.

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.

This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships. Although we will showcase the research of mathematicians who identify as women or gender minorities, this workshop is open to all.

This workshop will feature expository lectures about current developments in Diophantine geometry. This includes the uniform Mordell—Lang for rational points on curves, the Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

The theme of the conference will be explicit and computational methods in number theory and arithmetic geometry in a broad sense. The format will include scientific talks as well as time for informal collaboration and for coding projects related to (for example) PARI/GP, SageMath, Magma, OSCAR or the L-Functions and Modular Forms Database.

On the one hand, various topics where explicit computations have been the key for proving important results will be presented. These will be found in the context of modular forms, the study of rational points, as well as results towards the Birch and Swinnerton-Dyer conjecture. On the other hand, we will also focus on recently stated conjectures, for example the paramodular conjecture by Brumer and Kramer, and challenge participants to exhibit new examples to support such conjectures (in the case of the paramodular conjecture only one non trivial example is currently known).

We expect that the colloquium will lead to the emergence of new ideas and methods at the interface of these different fields, to new results as well as to new projects and collaborations.

This conference will be organized with the support of the National Research Agency in the framework of the project "MELODIA".

Speakers:

• Laura DeMarco (Chicago)
• Jonathan Pila (Oxford)
• Thomas Scanlon (Berkeley)
• Jacob Tsirmerman (Toronto)

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

A conference on Homotopy theory at Northwestern to honor the contributions of Paul Goerss.

ln this workshop, we will consider variants of Artin's primitive root conjecture leading to the study of the Galois groups of various radical extensions. Beyond the case of the multiplicative group studied by Lenstra and others, there are now also interesting results for elliptic radicals, and for division points in more general abelian varieties. ln this context, the elliptic analogue of Artin's conjecture is the Lang-Trotter conjecture, which is still open after more than 40 years.

The Galois representations associated to various division points in abelian varieties are central to understanding the Galois groups of the radical extensions that one tries to explicitly describe in this context, as they control the behaviour of the primes in the underlying problems. Understanding these Galois representations, and the entanglement between the extensions generated by different prime-power radicals, is essential to progress in this area.

ln this circle of problems and questions, one encounters interesting restrictions to local-global principles that will be addressed in this workshop, not only in the context of radical extensions.

A central topic in Diophantine Geometry is to understand how the geometry of a variety influences the arithmetic of its algebraic points, and conversely. Conjectures of Bombieri, Lang, and Vojta suggest that rational points of algebraic varieties satisfying suitable approximation conditions, are algebraically degenerate. On the other hand, conjectures on unlikely intersections suggest that algebraic points of special type —e.g. torsion points in semi-abelian varieties, special points in Shimura varieties— avoid subvarieties, unless the subvariety itself is also special (in a technical sense).

In recent years, a number of techniques have led to outstanding progress on Lang-Vojta conjectures, such as the Subspace Theorem, p-adic approaches to finiteness, and modular methods. Similarly, spectacular progress has been achieved on unlikely intersection conjectures thanks to new methods and tools, such as height formulas for special points, connections to model theory, refined counting results, and new theorems of Ax-Shanuel type (bi-algebraic geometry).

The goal of this workshop is to create the opportunity for these two groups to interact, to share their techniques, to update on the most recent progress, and to attack the outstanding open questions in the field.

The two directions described above are rather technical and specialized, and it seems necessary to bring together these groups of researchers to explain to each other not only the latest developments in their fields, but also the methods that made possible these breakthroughs. Thus, in this workshop we expect to have lectures explaining the main methods, as well as talks presenting the most recent progress in the subject by the world leading experts.

The Langlands program aims to relate systems of polynomial equations with integer coefficients to automorphic forms, i.e. functions on symmetric spaces with a large number of discrete symmetries. The focus of the trimester will be on some manifestations of this program, including:

moduli spaces of shtukas
p-adic techniques in local Langlands and the relation to geometric Langlands
Shimura varieties and more general spaces in global Langlands

The spring school serves an introduction to the conference "Arithmetic Statistics", and aims to provide PhD students and early stage researchers with the necessary background to enable them to fruitfully partake in the conference. lt will also be an occasion for Master students to have an introduction towards research in number theory.

Along with lecture courses, there will be exercise sessions and a possibility to work on small research projects under the guidance of the lecturers and the researchers proposing them.

The lecture courses will take place in the mornings, while exercise sessions will take place in the afternoon, with extra time allotted for round tables and work in groups.

Lecture courses thematics are the following:

• Galois representations and Diophantine equations,
• Complex Multiplication,
• Class field theory,
• Zeta functions and L-functions,
• Abelian varieties.

This school provides an introduction to some of the main topics of the trimester program. It is mainly directed at PhD students and junior researchers.

The theme of the conference is a type of number theory that has become very popular over the last decades, and that is influenced by the possibility of « experimentally » studying arithmetic objects with the help of a computer. Thanks to the wide availability of computer algebra systems, essentially any number theorist nowadays has this possibility at his fingertips. There are concrete objects that are not so easily determined « by hand », such as fundamental units in number fields of higher degree, or Mordell-Weil generators of point groups of elliptic curves, and a first impression of « what these typically look like » is often obtained by numerical experimentation.

Over the years, substantial datasets relating to number fields, elliptic curves and L-series have become available, enhancing our understanding of the arithmetic world somewhat beyond only the smallest examples, which may fail to show the true asymptotic behaviour.

Conference dedicated to the memory of Bas Edixhoven

This conference will be on various aspects of the local Langlands correspondence over p-adic fields and methods from p-adic Hodge theory. Topics will include the usual local Langlands correspondence, the p-adic local Langlands correspondence and the relation to coherent sheaves on spaces of Galois representations, and the geometry and cohomology of local Shimura varieties.

We are going to organize a week long conference during June 26-30, 2023, hosted by the Alfred Renyi Institute of Mathematics in Budapest, Hungary. The topic of the conference will emphasize the rich interactions between complex analysis and complex geometry, within the context of geometric analysis.

In addition, the conference will serve as an opportunity to celebrate the 70+1th birthday of Laszlo Lempert.

This will be a one week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.

This workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety does have any rational point at all.

This is a workshop with about 50 participants. Participation is by invitation. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions.

This conference will be on various aspects of the global Langlands correspondence. Topics will include in particular the geometry and cohomology of Shimura varieties and more general locally symmetric spaces, or moduli spaces of shtukas.

During the 2023-24 academic year the School will have a special program on the p -adic arithmetic geometry, organized by Jacob Lurie and Bhargav Bhatt, who will be the Distinguished Visiting Professor.

The last decade has witnessed some remarkable foundational advances in p-adic arithmetic geometry (e.g., the creation of perfectoid geometry and the ensuing reorganization of p-adic Hodge theory). These advances have already led to breakthroughs in multiple different areas of mathematics (e.g., significant progress in the Langlands program and the resolution of multiple long-standing conjectures in commutative algebra), have uncovered new phenomena that merit further investigation (e.g., the discovery of new structures on algebraic K-theory, new period spaces in p-adic analytic geometry, and new bounds on torsion in singular cohomology), and have made hitherto inaccessible terrains more habitable (e.g., birational geometry in mixed characteristic). This special year intends to bring together a mix of people interested in various facets of the subject, with an eye towards sharing ideas and questions across fields.