We are happy to announce that the Institut Mittag-Leffler will be hosting a research program entitled

"HIGHER ALGEBRAIC STRUCTURES IN ALGEBRA, TOPOLOGY AND GEOMETRY”

from January 10, 2022 to April 29, 2022.

Junior researchers (advanced PhD students or young postdocs) can apply for a fellowship to attend the program, covering all expenses (deadline: December 31, 2020). For all others, the program is by invitation only.

Institut Mittag-Leffler in Danderyd, just north of Stockholm, Sweden, is an international centre for research and postdoctoral training in mathematical sciences. The oldest mathematical research institute in the world, it was founded in 1916 by Professor Gösta Mittag-Leffler and his wife Signe, who donated their magnificent villa, with its first-class library, for the purpose of creating the institute that bears their name.

Program web page: http://www.mittag-leffler.se/langa-program/higher-algebraic-structures-algebra-topology-and-geometry

Junior research fellowships: http://www.mittag-leffler.se/research-programs/junior-fellowship-program

The organizers
Gregory Arone ([email protected])
Tilman Bauer ([email protected])
Alexander Berglund ([email protected])
Søren Galatius ([email protected])
Jesper Grodal ([email protected])
Thomas Kragh ([email protected])

The 2022 Simons Collaboration on Arithmetic Geometry, Number Theory and Computation Annual Meeting will focus on the following themes:

• Development and organization of software and databases supporting research in number theory and arithmetic geometry
• Fundamental research in arithmetic geometry inspired by computation and leading to new algorithms
• Explorations of L-functions, modular forms, and Galois representations with elegant and unusual properties

Talks will present contributions from members of the collaboration and work by leading experts that may inspire future developments.

The goal of the school is to present recent results in differential geometry related to PDEs, mathematical physics, and beyond. Lectures: Hamiltonian Fluid Dynamics; Continuum Mechanics of Media with Inner Structure; Introduction to Geometric Hydrodynamics; Fractalization and Quantization in Dispersive Systems; Symmetry, invariance, and equivalence in image processing; Introduction to Hamiltonian Mechanics, Monge–Ampère Geometry and the Navier–Stokes Equations.

64th meeting of the Texas Geometry and Topology Conference, to take place at the University of Texas at Dallas from February 25 - 27, 2021.

SPEAKERS

The invited speakers are as follows:

Sun-Yung Alice Chang (Princeton University)

John Etnyre (Georgia Tech University)

David Gabai (Princeton University)

Mark Haskins (Duke University)

Bruce Kleiner (New York University)

Vladimir Markovic (Oxford University)

William Minicozzi (Massachusetts Institute of Technology)

Andre Neves (University of Chicago)

Peter Oszvath (Princeton University)

Antoine Song (University of California, Berkeley)

This conference, which is the 45th iteration of the Midwest Representation Theory Conference, will focus on recent progress in the theory of representations of groups over local fields as well as connections of this theory to other areas within mathematics, notably number theory and geometry. Please see the conference page at https://homepage.divms.uiowa.edu/~mkrishna/2022mrtc.

If you are interested in attending, then please apply to participate at https://forms.gle/qT9qAUFoiMxm2mcB6. This application is available until February 14.

If you are interested in giving a contributed talk, please apply via https://forms.gle/Baxuz4qAA8XHVFKKA. Review of applications for contributed talks will begin February 7.

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.

Discrete mathematics is a branch of the mathematical sciences which poses a wide range of challenging research problems in its own right and gives rise to important applications in other fields. This 3rd IMA conference on discrete mathematics, following on from the previous two at Derby, will consider a range of aspects of discrete mathematics, both pure and applied. It is open to researchers working with mathematical structures and abstract constructs, and to those involved in the theory and practice of discrete mathematics. Results which establish links between different areas of discrete mathematics are welcomed, as are applications and the development of new tools. The purpose of this event is to highlight progress in the field through the development of novel theories, methodologies, and applications accordingly, and to inspire future work. Topics of discrete mathematics including, but not limited to, the following: Graph Theory; Extremal Combinatorics: Additive Combinatorics: Probabilistic Combinatorics: Enumerative and Analytic Combinatorics: Matroids: Combinatorial Algorithms: Designs and Finite Geometries: Ordered and partially ordered sets: Set Systems: Combinatorial optimisation: links with related areas including discrete probability and number theory: Applications. Call for Papers: Papers will be accepted (or not) for the conference based on a short 300 word abstract for oral presentation. Abstracts should be submitted online at https://my.ima.org.uk. If your abstract is a less conventional part of discrete mathematics, please try to make clear how your abstract relates to discrete mathematics. Please state whether your title is intended for oral or poster presentation (poster presentations are optional). Oral presentations are expected to be 25 minutes in length, including 5 minutes for questions and answers. CLOSING DATE- 14 January 2022 Acceptance Notification – 28 January 2022 Conference Fees: Early Bird Fees*: IMA Member £220 Non‐IMA Member £300 IMA Student £150 Non‐IMA Student £160 *Early Bird Fees will be available until Monday 7 March 2022, after which the fees will rise by £20.

Conference fees include refreshments and lunches throughout the conference, facilities hire and a drinks reception on Monday evening.

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. CLOSING DATE – 25 March 2022 Confirmed Invited Speakers: Prof Simon Blackburn, Royal Holloway Dr Jessica Enright, University of Glasgow Prof James Hirschfeld, University of Sussex Dr Eoin Long, University of Birmingham

Organising Committee: Dr David Penman, University of Essex (chair) Prof Peter Cameron, University of St. Andrews Prof Peter Larcombe, University of Derby Dr Bridget Webb, Open University

The Geometry Festival is an annual three-day event celebrating geometry and highlighting recent advances in geometry and related fields. Everyone is invited to the Geometry Festival, and graduate students are especially encouraged to attend! Due to the ongoing pandemic, we can’t host the Festival in person this year, but we hope to welcome you all virtually.

Periods occur in various branches of mathematics and as the title of our conference indicates, their study intertwines arithmetic, Diophantine analysis, differential equations, and algebraic geometry. Many interesting results have been proved in recent years and many challenging problems on periods are still open. The aim of our conference is to bring together specialists who cover all these different points of view and their ramifications, with special attention towards possible applications to broader areas of the techniques developed in the study of periods and their realizations.

Yves André has contributed in many ways to this ongoing adventure and this conference will not only be the opportunity to listen to a broad range of recent developments in mathematics around the topic of periods, but also to celebrate his 60th birthday.

The meeting will not be online.

Speakers include: Francesca Balestrieri, Jen Berg, Tim Browning, Yang Cao, Jean-Louis Colliot-Thélène, Jordan Ellenberg, Roger Heath-Brown, Marta Pieropan, Bjorn Poonen, Damaris Schindler, Alexei Skorobogatov, Olivier Wittenberg.

Details: The topic of rational points on varieties over the rational numbers is the modern perspective on the theory of Diophantine equations.

There is a good (partially conjectural) understanding now of the situation for algebraic curves. The proof of the Mordell conjecture for curves of genus at least 2 by Faltings is one of the crowning achievements in the area, and much of the work on elliptic curves is driven by the Birch-Swinnerton-Dyer conjecture. Recent highlights include the work of Bhargava and his collaborators on average ranks of elliptic curves. The situation in higher dimensions is much murkier however.

The aim of the meeting is to bring together leading experts and early career researchers to make progress on understanding rational points on surfaces and higher dimensional varieties. Traditionally there have been two separate communities working in the area, using tools from analytic number theory and algebraic geometry, respectively. Spectacular progress has been made in recent times by managing to bridge these communities, with a particular highlight being applications of Green-Tao-Ziegler's work on primes in arithmetic progressions to the fibration method. The emphasis in the meeting will be on building upon this bridge and further inspiring collaboration between the analytic and geometric communities.

Specific topics to be covered will include the following:

Schinzel's Hypothesis with probability Campana points. Purity of strong approximation. Rational points in families. Brauer--Manin obstruction.

The workshop aims to bring together researchers from various areas around anabelian geometry, very broadly construed. The workshop will be held (tentatively in-person) on April 30 and May 1, on the UGA campus.

3 – 5 May 2022 International Centre for Mathematical Sciences, Edinburgh

https://ima.org.uk/18111/3rd-ima-conference-on-inverse-problems-from-theory-to-application/

CALL FOR PAPERS

Inverse problems are widespread in many varied fields such as medical and satellite imaging, biology, astronomy, geophysics, environmental sciences, computer vision, energy, finance, and defence. These problems are inverse in the sense that they arise from seeking to use a mathematical or physical model “backwards” to indirectly determine a quantity of interest from the effect that this quantity causes on some observed data.

A main challenge resulting from using models “backwards” to measure causes from their effects is that solutions are often not well posed, i.e., not unique and/or unstable with respect to small perturbations in the data. This difficulty has stimulated an important amount of research and innovation at the interface of applied mathematics, statistics, engineering, physics, and other fields, leading to great social and economic benefit through impact on science, medicine, and engineering.

The aim of this conference is to bring together the applied mathematics, statistics, machine learning, engineering, physics and industrial communities around the topic of inverse problems to discuss recent developments and open challenges in theory, methodology, computational algorithms, and applications. We welcome industrial representatives, doctoral students, early career and established academics working in this field to attend. Topics of interest include, for example, • Inverse problems in mathematical and computational imaging. • Inverse problems in science, medicine, engineering, and other fields. • Model‐based and data‐driven methods for solving inverse • Optimisation, statistical, and machine learning methods for solving inverse problems. • Mathematical theory for inverse problems. • Deterministic and stochastic computational methods and algorithms.

Call for Papers instructions: Call for Papers ‐ Papers will be accepted for the conference based on a 100 word abstract for oral or poster presentation. We welcome abstracts to be submitted by 7th January 2022 via https://my.ima.org.uk./. Please indicate whether your title is intended for oral “presentation” or “poster” presentation. Please send your abstracts in plain text format (no equations).

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

Registration will close on 27 April 2022, for any enquiries after this date please contact the Conferences Team. 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: Conference fees include access to the Conference, refreshments and lunches and a Delegate pack. Early Bird Fee – IMA Member £200 Early Bird Fee – Non Member £265 Early Bird Fee – IMA Student £100 Early Bird Fee – Non Member Student £120

Early Bird Fees will be available until 9th of April after which fees will increase by £20.

Confirmed Invited Speakers: Thomas Pock (Graz University of Technology, Austria) Gabriele Steidl (Berlin Institute of Technology, Germany) Jason McEwen (University College London & Kagenova) Yi Yu (University of Warwick, UK) Andrew Duncan (Imperial College London, UK) Luca Calatroni (CNRS & Nice University, France)

Organising Committee: Marcelo Pereyra (Heriot‐Watt University & Maxwell Institute) ‐ Conference Chair Yoann Altmann (Heriot‐Watt University) Konstantinos Zygalakis (University of Edinburgh & Maxwell Institute) Mike Davies (University of Edinburgh)

Scientific Committee: Simon Arridge (University College London) Marta Betcke (University College London) Martin Benning (Queen Mary University of London) Thomas Blumensath (University of Southampton) Tatiana Bubba (University of Bath) Julie Delon (Paris Descartes University) Matthias Ehrhardt (University of Bath) Jean‐François Giovannelli (University of Bordeaux) Sean Holman (University of Manchester) Clifford Nolan (University of Limerick) Clarice Poon (University of Bath) Audrey Repetti (Heriot‐Watt University & Maxwell Institute)

Further information: For further information on this conference, please visit the conference webpage: https://ima.org.uk/18111/3rd-ima-conference-on-inverse-problems-from-theory-to-application/

Contact information: For scientific queries please contact: Marcelo Pereyra (Heriot Watt University) [email protected]

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

The Cornell Topology Festival is a three-day annual conference showcasing recent developments in topology and allied areas.

Signal processing and machine learning constitutes an important area for the application of mathematical concepts and techniques, in an era where learning algorithms must be transparent, robust, explainable and understandable, and ethical. It is a thriving area, as demonstrated by the success of the UK hosting the recent International Conference on Acoustics, Speech, and Signal Processing (ICASSP) in Brighton in 2019.

Signal and information processing is at the heart of our technological world, fuelled by developments in, for example, mobile communications, networks and graphs, multimedia systems, medical image analysis, genomics and bioengineering, neural signal processing, big data processing and internet of things. The aim of the conference is to bring together mathematicians, statisticians and engineers with a view to exploring recent developments in mathematics for signal processing and machine learning and identifying fruitful avenues for further research. It is hoped that the meeting will help to attract more mathematicians into this important and challenging field. The conference will follow the same successful format as our previous conferences, comprising tutorials, keynote addresses and non-overlapping technical sessions consisting of oral and poster presentations. A social programme will be organised and will include a reception to welcome delegates.

The Franco-Asian summer school on arithmetic geometry is a continuation of the many fruitful joint France-Asia events that have taken place since the Asian Year on Motives initiated by Jean-Marc Fontaine at IHES in 2006. These collaborations have had a considerable impact on the international development of fundamental branches of arithmetic geometry. This new event, organized at CIRM, will be open to students and young researchers from all over the world. It will consist in four mini-courses and several lectures.

Pre-registration on the web is mandatory for all participants who wish to attend the summer school in person at CIRM. The number of participants is limited to 90. Please complete the pre-registration form here:

http://www.cirm-math.fr/preRegistration/index.php?EX=menu0&id_renc=2534

WINGs 2022 is the second instalment of an annual retreat for women, and other underrepresented genders, in number theory and geometry. It is aimed at early career mathematicians, from PhD onwards. Events include social activities and short talks for participants to encourage interaction and learn about each other’s research and interests. We aim to counteract the isolation which can be experienced by female mathematicians during their career by fostering a sense of community from the start.

This conference is aimed towards early graduate students and advanced undergraduate students interested in algebraic geometry, commutative algebra, geometric group theory, and number theory.

The goal of this conference is to:

Foster a sense of community amongst underrepresented groups in mathematics,
Introduce possible research areas,
Expose the participants to role models and possible mentors.

We have funding to provide for travel and accommodation for about 40 participants, priority is given to participants from underrepresented groups. An application for funding will be available soon.

This conference is part of the RTG: Algebra, Geometry and Topology at the University of Utah funded by the NSF RTG grant #1840190.

European Women in Mathematics/European Mathematical Society Mittag-Leffler Summer School Chromatic Homotopy Theory and Friends is scheduled to take place June 7 to 10, 2022 at the Mittag-Leffler Institute in Djursholm, Sweden.

The goal of this summer school is to increase the number of women mathematicians working in chromatic homotopy theory and adjacent areas. The summer school will be centered around a background lecture series by Constanze Roitzheim from the University of Kent on chromatic homotopy theory, with satellite talks in areas of active research related to the central topic.

As a European Women in Mathematics Summer School, we aim to have at least 50% women among the participants.

Please visit

https://docs.google.com/forms/d/e/1FAIpQLScQz5DZ2iFwHEWxs8CVMBa_xR77GxJpm3L3Z6wxu7J2Ukm0Xg/viewform

for more information and the application form.

The application deadline is December 15, 2021.

A conference bringing together established and junior researchers from the Langlands Program and Homotopy Theory.

CALL FOR ABSTRACTS/PAPERS This conference on financial mathematics will be focusing on pressing challenges in finance and insurance produced by climate change, demographic developments, and the ever-increasing dominance of data and information. Alongside the challenges, this three-day conference’s goal will devote time to the role and responsibilities financial and insurance mathematics have in developing solutions and in assisting with transitions necessary to mitigate irreversible adverse environmental and socio- economic impact. The aim is to promote interdisciplinary cooperation bridging mathematics, statistics and computer science with finance, climate science, insurance and economics. Industry professionals and members of government agencies will be invited to share their experience and expertise alongside academic experts in the field in order to scope out the most urgent research directions with the highest potential for incisive solutions.

On this basis we invited academics and practitioners to submit papers to the Conference in the following fields: ● Mathematical Finance Interest Rates and Credit Risk, Systemic Risk, Model Risk and Uncertainty, Game Theory/Mean Field Games, Stochastic Modelling of Epidemics (or Climate), and more. ● Actuarial Science Extreme events, Pensions/Annuities, Mortality (COVID implications), New Insurance Paradigms, Population mortality modelling, and Risk Measures and more. ● Climate Change Risk Climate Risk, Extreme events, Transition Risk, Population displacement and migration, Stranded assets and more. ● Digital Finance Mobile money, Fintech/Insurtech, Cyber Risk, Decentralization of financial flows, Cryptocurrencies, Telematics and more. ● Green Energy and Finance Green Bonds and Renewable Investment, Smart Grid, Distributed Energy Systems and Micro-grid, Emission Trading, Renewable Energy, Electric and Hybrid Vehicles, Smart Storage and more.

Confirmed Invited Speakers: Fabio Angelo Maccheroni, Università Bocconi Markus Leippold, University of Zurich, Department of Banking and Finance Luitgard Veraart, London School of Economics and Political Science Catherine Donnelly, Heriot Watt University

Call for Abstracts instructions: Talks will be accepted for the conference based on a 350 word abstract. Abstracts should be submitted by 15th January 2022 either online at http://online.ima.org.uk or by e‐mail to [email protected] Authors will be notified by 15th February 2022 if their abstract has been accepted for oral or poster presentation.

Oral presentations are expected to be 25 minutes in length, including time for questions and answers.

Abstracts should include: ● Whether your title is intended for oral or poster presentation. ● Title of the talk ● Authors and Affiliations ● Intended Speaker ● 350 words describing talk

Call for Papers instructions: Authors may consider submitting full papers based on their abstract for publication in a special issue of the IMA Journal of Management Mathematics, titled “Mathematics of Finance and Climate Risk”. The topic for papers must be climate‐related. Authors must follow general instructions for the journal: https://academic.oup.com/imaman/pages/General_Instructions and will be peer‐reviewed according to journal policy.

The deadline for submitting a final version of the paper will be 31st June 2022. Authors should submit their paper to the journal in the usual way and select “Mathematics of Finance and Climate Risk” as the special issue.

Authors do not have to submit a paper to the special issue to be able to present in the conference.

Registration 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. Registration Deadline – 31 May 2022

Conference Fees: Early Bird Conference Fee – Non-IMA Member £385 Early Bird Conference Fee – IMA Member £345 Early Bird Conference Fee – IMA Student £170 Early Bird Conference Fee – Non-IMA Student £200 £20 will be added to the early bird conference fee on the 9th of May

Organising Committee: Corina Constantinescu, University of Liverpool Paul Johnson, University of Manchester Andrea Macrina, University College London

Contact information: For scientific queries please contact: Paul Johnson, [email protected]

For general conference queries please contact Maya Everson, Conference Officer E‐mail: [email protected] Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend‐on‐Sea, Essex, SS1 1EF, UK.

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 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 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.

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]

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.

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.

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 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 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 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).

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.

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.

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

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".

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.

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.

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 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.