The 38th Annual Workshop in Geometric Topology will be held online June 15-17, 2021. The featured speaker will be Peter Bubenik of the University of Florida, who will give a series of three one-hour lectures on Topological Data Analysis.

Participants are invited to contribute talks of 20 minutes. Contributed talks need not be directly related to the topic of the principal lectures. Title and abstracts must be submitted by May 15. If there are more volunteers to speak than there are time slots, the organizers will choose talks that provide a balanced collection of topics and respect the historical traditions of the workshop. Earlier responses may be given some preference. Applicants will be notified whether their talk has been accepted by June 1.

Full details, including registration and information about submitting titles and abstracts for contributed talks, can be found at the conference web site at http://faculty.tcu.edu/gfriedman/GTW2021

The Workshops in Geometric Topology are a series of informal annual research conferences that have been held since 1984. In non-pandemic years, the workshops currently rotate among Brigham Young University, Calvin College, Colorado College, Texas Christian University, and the University of Wisconsin at Milwaukee. Each workshop features a series of three lectures by one principal speaker, providing a substantial introduction to an area of current research in geometric topology. Participants are invited to contribute short talks on their own research, and there is ample time set aside each day for informal interactions between participants. Funding for the workshop series is currently provided by a grant from the National Science Foundation (DMS-1764311).

Workshop Organizers: Fredric Ancel, University of Wisconsin-Milwaukee Greg Friedman, Texas Christian University Craig Guilbault, University of Wisconsin-Milwaukee Molly Moran, Colorado College Nathan Sunukjian, Calvin College Eric Swenson, Brigham Young University Frederick Tinsley, Colorado College Gerard Venema, Calvin College

Organized online by the Azat Miftakhov committee

Wednesday June 16, 2021 starting at 4pm Central European Summer Time (UTC+2)*

In solidarity with Azat Miftakhov, a graduate student from Moscow State University who has been arbitrarily detained by Russian state authorities for almost two years and half.

4pm Cédric Villani (Member of the French National Assembly)

Opening speech

4:15 pm Maryna Viazovska (École Polytechnique Fédérale de Lausanne, Switzerland)

TBA

5:15 pm Alexander Bufetov (CNRS & Institut de Mathématiques de Marseille, France & Steklov, IITP RAS, Russia)

Determinantal point processes: quasi-symmetries, minimality and interpolation

6:15 pm Peter Scholze (Universität Bonn, Germany)

Condensed Mathematics

• Tokyo at 11pm, Moscow at 5pm, Bonn, Paris and Warsaw at 4pm, London at 3pm, New York at 10am, San Francisco at 7am

The webinar will be broadcast live on several websites whose addresses will be announced a few days before on this webpage (https://caseazatmiftakhov.org/)

Since their introduction 50 years ago, the notions of infinity-algebras (Stasheff), operads (May), model categories (Quillen), and higher categories (Boardman-Vogt) gave rise to powerful tools which made possible the resolution of open problems and prompted revolutions in many domains like algebraic topology (rational homotopy theory, faithful algebraic invariants of the homotopy type of spaces), deformation theory (formality theorems, formal moduli problems), and mathematical physics (quantisation of Poisson manifolds, quantum field theories), to name but a few. This theory of higher structures using operadic calculus is currently under rapid development and there is a need today to provide the community with a modern state of the art; this is the main goal of the present workshop, which will be accessible to a wide audience.

This virtual workshop will focus on recent advances in Geometry and Mathematical Physics, with lectures by senior faculty at Boston University, Keio University, and Tsinghua University. There will be three talks per day. All talks will be accessible to advanced graduate students in the areas of algebraic geometry, differential geometry, symplectic geometry and related areas of mathematical physics. Please see the URL for more details. Please be sure to register, so that you can get a Zoom link to the talks.

Applied and computational topology, one of the most rapidly growing branches of mathematics, is becoming a key tool in applied sciences. It is making impact not only in mathematics, but on the wide interdisciplinary environment including material and medical sciences, data science, robotics. Building upon successful conferences held in Bedlewo in 2013 and 2017, the next edition of Applied Topology in Bedlewo will take place in 2021. Similarly as before, our aim is to bring together scientists from all over the world working in various fields of applied topology. This time we will focus on:

• random topology,
• topological methods in combinatorics,
• topological data analysis and shape descriptors,
• topological analysis of time-varying data in biology, engineering and finance,
• topological and geometrical descriptors of porous materials.

This workshop is one of four workshops of special RIMS year "Expanding Horizons of Inter-universal Teichmüller Theory".

The workshop will review fundamental developments in anabelian geometry and report on numerous recent developments.

Anabelian geometry, together with higher class field theory and Langlands correspondences, is one of three fundamental generalisations of class field theory.

In this Masterclass, we will learn about the high dimensional cohomology of moduli spaces such as the moduli space of curves, graphs, and lattices. These moduli spaces are classifying spaces of groups such as mapping class groups, automorphism groups of free groups, and arithmetic groups. We will learn about duality groups whose high dimensional cohomology of these moduli spaces is related to the low degree homology groups with twisted coefficients. We will also discuss graph homology and tropical curves.

The masterclass is aimed at advanced graduate students and postdocs with an interest in algebraic topology and geometric group theory. Connections with algebraic geometry and number theory will be mentioned but this is not the primary focus.

In arithmetic geometry, one studies solutions to polynomial equations defined with arithmetically interesting coefficients, such as integers or rational numbers. One way to study such objects, which has seen tremendous success in the last several decades, is by investigating their symmetries. Quite surprisingly, in several interesting situations, many of the geometric and arithmetic properties of the objects in question are actually controlled by the object’s symmetries.

Unfortunately, it is usually impossible to study these symmetries directly with current technology. To get around this, mathematicians working in this area often study simplified (often linearized) versions of the symmetries in question, which still capture a significant amount of information about the given object. This workshop will bring together both senior and junior researchers, including graduate students, postdocs, and leading experts, who study objects of geometric and arithmetic origin from the point of view of their symmetries and their linearized variants.

This workshop is one of four workshops of special RIMS year "Expanding Horizons of Inter-universal Teichmüller Theory".

Combinatorial anabelian geometry concerns the reconstruction of scheme- or ring-theoretic objects from more primitive combinatorial constituent data. In this sense, it is closely philosophically related to inter-universal Teichmüller theory.

The purpose of the present workshop is to expose fundamental, introductory aspects of combinatorial anabelian geometry, as well as more recent developments related to the Grothendieck-Teichmüller group and the absolute Galois groups of number fields and mixed-characteristic local fields.

The workshop will also treat results concerning the "resolution of nonsingularities" of hyperbolic curves over mixed-characteristic local fields, such results are closely related to combinatorial anabelian geometry over mixed-characteristic local fields.

The purpose of this conference is to bring together experts from across automorphic forms, representation theory, and arithmetic connected to the theory of theta series and the theta correspondence in order to survey the most recent developments and to open up future courses of investigation. This conference marks the 70th birthday of Steve Kudla, whose mathematical work has made a profound impact on the themes of this conference.

There is an age-old relationship between arithmetic and geometry, going back at least to Euclid's Elements. Historically, it has usually been geometry that has been used to enrich our understanding of arithmetic, but the purpose of this workshop is to study the flow of information in the other direction. Namely, how can arithmetic enhance our understanding of geometry? This meeting will bring together researchers from both sides of the partnership, to explore ways to bind the two fields ever closer together.

RNT2 will be a remote collaborative research experience for the weeks of July 12 through 23. 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. 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. 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.

One focus of modern number theory is to study symmetries of numbers that are roots of polynomial equations. Collections of such symmetries are called Galois groups, and they often encode interesting arithmetical information. The theory of Galois representations provides a way to understand these Galois groups and in particular, how they interact with other areas of mathematics. This workshop will investigate how these Galois representations can be put together into families, and search for new arithmetic applications of these families.

The workshop will bring together people attacking key problems in number theory via techniques involving concrete or computable descriptions. Here, number theory is interpreted broadly, including algebraic and analytic number theory, Galois theory and inverse Galois problems, arithmetic of curves and higher-dimensional varieties, zeta and L-functions and their special values, and modular forms and functions. Considerable attention is paid to computational issues, but the emphasis is on aspects that are of interest to the pure mathematician.

During the last two weeks of July 2021, the University of Oregon will host a graduate instructional workshop followed by a collaborative research workshop to promote diverse collaborations.

While both of these workshops focus on algebraic and p-adic aspects of automorphic forms, L-functions, and related topics, the two workshops are independent. Applicants are encouraged to apply for one or both of the workshops, and funding decisions will be determined separately for each.

This is the summer school part of the LMS-INI-Bath Symposium on K-theory and Representation Theory (which will take place in July 2022). In this summer school, we will cover material that is foundational to the upcoming symposium, namely, representation theory of real and p-adic Lie groups, the theory of C*-algebras and operator K-theory, and finally the method of "Dirac Induction" which brings the above together by employing Dirac operators in the study of representations.

Algebraic dynamics is the study of discrete dynamical systems on algebraic varieties. It has its origins in complex dynamics, where one studies self-maps of complex varieties, and now encompasses dynamical systems defined over global fields.

In recent years, researchers have fruitfully investigated the latter by applying number-theoretic techniques, particularly those of Diophantine approximation and geometry, subfields which study the metric and geometric behavior of rational or algebraic points of a variety. The depth of this connection has allowed the mathematical arrow between the two fields to point in both directions; in particular, arithmetic dynamics is providing new approaches to deep classical Diophantine questions involving the arithmetic of abelian varieties. This workshop will focus on communicating and expanding upon the connections between algebraic dynamics and Diophantine geometry. It will bring together leading researchers in both fields, with an aim toward synthesizing recent advances and exploring future directions and applications.

The ICREM is a biennial conference series organised by the Institute for Mathematical Research (INSPEM), Univeristi Putra Malaysia, since its inaugural in 2003. With the joint efforts from our distinguished partners, the ICREM5 and ICREM8 were successfully organised by the Institut Teknologi Bandung (ITB), Indonesia in 2011 and 2017 respectively. The ICREM6 was successfully organized by the Institute of Mathematics, Vietnam Academy of Science & Technology (IMVAST), Vietnam in 2013.

This year, INSPEM with ITB, IMVAST, Thai Nguyen University of Education, Vietnam (TNUE), and Universität der Bundeswehr München, Germany (UniBw) are delighted to announce that the 9th International Conference on Research and Education in Mathematics (ICREM9) will be held in the beautiful island of Langkawi, MALAYSIA, from 02 - 06 August 2021.

The ICREM9 will have five Satellite Conferences:

• Satellite Conference on Computational Fluid Dynamics (CFD2021)
• Satellite Conference on Artificial Intelligence & Data-Driven Innovations (AIDDI2021)
• Satellite Conference on Scientific Computing, Simulation, and Quantitative Instrumentation (SCSQI2021)
• Satellite Conference on Structural and Analytical Mathematics with Cryptology (SAMC2021)
• Satellite Conference on Literacy (LE2021)

The Organising Committee is looking forward to welcoming the delegates to the ICREM9 held for the first time in the beautiful island known as The Jewel of Kedah (Langkawi Permata Kedah). We are working towards preparing an attractive scientific programme with diverse topics to create a conducive environment suitable for encouraging and facilitating our delegates to share their knowledge and exchange ideas in all aspects of mathematics and its application.

The venue of the conference is the perfect setting to complement the ICREM9. Langkawi is an archipelago made up of 99 islands in the Malacca Strait some 30 km off the mainland coast of northwestern Malaysia. The islands are a part of the state of Kedah, which is adjacent to the Thai border. Surrounded by the turquoise sea, the interior of the main island is a mixture of picturesque paddy fields and jungle-clad hills. The main island spans about 25 km from north to south and slightly more for east and west. The coastal areas consist of flat, alluvial plains punctuated with limestone ridges. Two-thirds of the island is dominated by forest-covered mountains, hills, and natural vegetation. The island's oldest geological formation, the Machinchang Formation, was the first part of Southeast Asia to rise from the seabed in the Cambrian more than half a billion years ago.

We invite you to discover for yourself our little treasures. We are honoured to host the ICREM9 here in Langkawi, Malaysia. It is our hope that you will join us and learn, enjoy, and most importantly be a part of the ICREM9 community. Organise a session, give a talk, and remember to experience this great island.

The Organising Committee is looking forward to playing host to all members of the mathematical community at the ICREM9 Conference.

See you in Langkawi, MALAYSIA for ICREM9!

Details see conference website.

The GTA 2021 conference will bring together world class researchers in mathematics. Its main objectives are to discuss recent advances in the fields of algebraic geometry, number theory and their applications, as well as to foster international collaborations on connected topics.

Although contributions from all related areas of mathematics are welcome, particular emphasis will be placed on research interests of our late colleague Alexey Zykin, namely: zeta-functions and L-functions, algebraic geometry over finite fields, families of fields and varieties, abelian varieties and elliptic curves.

This is the meeting of the SIAM Activity Group on Algebraic Geometry.

The purpose of the SIAM Activity Group on Algebraic Geometry is to bring together researchers who use algebraic geometry in industrial and applied mathematics. "Algebraic geometry" is interpreted broadly to include at least: algebraic geometry, commutative algebra, noncommutative algebra, symbolic and numeric computation, algebraic and geometric combinatorics, representation theory, and algebraic topology. These methods have already seen applications in: biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear partial differential equations, optimization, robotics, and statistics. We welcome participation from both theoretical mathematical areas and application areas not on this list which fall under this broadly interpreted notion of algebraic geometry and its applications.

Y-RANT is a (relatively) new conference aimed at postgraduate students and early career researchers in algebraic number theory, promoting discussion and sharing of ideas between members of the community. Participants are strongly encouraged to register to give short talks on their research or other topics of interest. We will do our best to accommodate all participant's talks, however this might not be possible due to time constraints. In addition there will be three keynote talks given by senior researchers in the field.

Despite the enormous commercial potential that quantum computing presents, the existence of large-scale quantum computers also has the potential to destroy current security infrastructures. Post-quantum cryptography aims to develop new security protocols that will remain secure even after powerful quantum computers are built. This workshop focuses on isogeny-based cryptography, one of the most promising areas in post-quantum cryptography. In particular, we will examine the security, feasibility and development of new protocols in isogeny-based cryptography, as well as the intricate and beautiful pure mathematics of the related isogeny graphs and elliptic curve endomorphism rings. To address the goals of both training and research, the program will be comprised of keynote speakers and working group sessions.

A conference on the occasion of Takeshi Saito's 60th birthday

The conference Arakelov Geometry is organized by José Ignacio Burgos Gil, Walter Gubler, and Klaus Künnemann. This conference constitutes the eleventh session of the Intercity Seminar on Arakelov Theory organized by José Ignacio Burgos Gil, Vincent Maillot and Atsushi Moriwaki with previous sessions in Barcelona, Beijing, Copenhagen, Kyoto, Paris, Regensburg, and Rome.

This Conference has been organised in cooperation with the Society for Industrial and Applied Mathematics (SIAM).

Areas of interest include, but are not limited to: Topology. Kinematics. Algebraic topology of con?guration spaces of robot mechanisms. Topological aspects of path planning and sensor networks. Differential topology and singularity theory of robot mechanism and moduli spaces. Algebraic Geometry. Varieties generated by linkages and constraints. Geometry of stiffness and inertia matrices. Rigid-body motions. Computational approaches to algebraic geometry. Dynamical Systems and Control. Dynamics of robots and mechanisms. Simulation of multi-body systems, e.g. swarm robots. Geometric control of robots. Optimal control and other optimisation problems. Combinatorial and Stochastic Methods. Rigidity of structures. Path planning algorithms. Modular robots. Statistics. Stochastic control. Localisation. Navigation with uncertainty. Statistical learning theory. Cognitive Robotics. Mathematical aspects of Artificial Intelligence, Developmental Robotics and other Neuroscience based approaches.

Invited speakers: Dr Mini Saag – University of Surrey, UK Prof Frank Sottile - Texas A&M University, USA Prof Stefano Stramigioli - University of Twente, The Netherlands

A lattice is a discrete collection of regularly ordered points in space. Lattices are everywhere around us, from the patterned stacked arrangements of fruits and vegetables at the grocery to the regular networks of atoms in crystalline compounds. Today lattices find applications throughout mathematics and the sciences, applications ranging from chemistry to cryptography and Wi-Fi networks.

The focus of this meeting is the connections between lattices and number theory and geometry. Number theory, one of the oldest branches of pure mathematics, is devoted to the study properties of the integers and more sophisticated number systems. Lattices and number theory have many deep connections. For instance using number theory it was recently demonstrated that certain packings of balls in high dimensions are optimally efficient. Lattices also appear naturally when one studies certain spaces that play an important role in number theory; one of the main focuses of this meeting is to investigate computational and theoretical methods to understand such spaces and to expand the frontier of our algorithmic knowledge in working with them.

The cohomology of arithmetic groups is the study of the properties of ``holes'' in geometric spaces that contain information about number theory. The workshop will bring together mathematicians with expertise in number theory, topology, and geometric group theory to tackle these problems and explore recent developments.

The Maple Conference 2021 - Maple in Mathematics Education and Research

This FREE virtual conference is dedicated to exploring different aspects of the math software Maple, including Maple's impact on education, new symbolic computation algorithms and techniques, and the wide range of Maple applications. Attendees will have the opportunity to learn about the latest research, share experiences, and interact with Maple developers.

The conference will take place online, and will include live presentations and discussions as well as recordings and chatrooms, in order to accommodate time zones. Maplesoft staff will also offer Maple training sessions on a variety of topics during the conference.

All presenters at the conference are invited to submit a full paper. These submissions undergo peer-review, and the decision about acceptance or rejection lies with the Program Committee. Accepted papers are published in the conference proceedings.

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])

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.

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.

Arithmetic geometry is a broad and central area of Mathematics. The summer school will focus on a number of areas of important progress over the last three or four years, notably: p-adic Hodge theory, Ramification of étale l-adic sheaves, Homotopical algebra techniques and applications to motives and epsilon factors. The summer school will consist of 4 mini-courses supplemented by ten one-hour lectures.

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

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.

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 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.

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.