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 purpose of this school is to familiarise advanced Master’s students, Ph.D. students and early career researchers with the central themes of research in arithmetic geometry,and teach them both classical and state-of-the-art tools in the field. The research school is an introduction to the conference SAGA, “Symposium on Arithmetic Geometry and its Applications” and it consists of four 3-day mini-courses, taught by teams of internationally renowned researchers, who are known to be excellent teachers.

Courses:

• Galois representations and modular forms: Alex Ghitza and Anna Medvedovsky
• Modularity and diophantine applications: Samir Siksek and Samuele Anni
• Local-global principles: Rachel Newton and Ekin Ozman
• Jacobians and models: Tim Dokchitser and Elisa Lorenzo García

The masterclass will present spectacular recent advances in motivic filtrations and their applications. To briefly put this in context, every cohomology theory, in arithmetic geometry and elsewhere, should arise as the graded pieces of a motivic filtration of some localizing invariant, algebraic K-theory and topological cyclic homology being notable examples. The definition of the appropriate motivic filtrations, however, was long elusive. Voevodsky received the 2002 Fields medal, in part, for his definition of the motivic filtration of algebraic K-theory of schemes smooth over a field. This definition, however, was based on algebraic cycles, which are notoriously difficult to handle. In 2018, Bhatt, Morrow, and Scholze defined a motivic filtration of p-complete topological cyclic homology in an entirely different way, which is much simpler and easier to employ elsewhere, and this breakthrough has led to numerous advances.

Building on work of Antieau, Morin, and, independently, Bhatt-Lurie, have refined the Bhatt-Morrow-Scholze filtration to a filtration of non-completed topological cyclic homology, and Morin discovered that its graded pieces precisely account for an archimedean factor in a conjectural formula for the special values of the Hasse-Weil zeta function of a regular scheme, proper over the integers. It is very exciting to see that such quantative archimedean information can be extracted from topological cyclic homology! More recently, Hahn-Raksit-Wilson introduced the even filtration, and showed that it accounts for both the Bhatt-Morrow-Scholze filtration and the Morin and Bhatt-Lurie refinements thereof. It might also recover and extend Voevodsky's filtration?

The thematic month “Arithmetic and Information Theory” focuses on arithmetic geometry, information theory and their interplay.

Arithmetic geometry is a fundamental and growing area of research in modern mathematics, deeply connected to almost all of its branches. As a measure of its importance, about a quarter of the Fields medalists have worked on problems in arithmetic geometry. There is a vast number of different techniques that have been developed in the field. Algebraic Geometry Codes Theory studies (amongst others) varieties, and in particular curves, with many rational points, having in mind that maximal curves are the aspirational target to obtain codes with the best correction rate. This maximality corresponds to extremal points in the distribution of the Frobenius endomorphism acting on the Tate module of the Jacobian of the curves. For elliptic curves, we are confronted with the Sato-Tate conjecture which is concerned with the statistics to modulo p reductions of families of elliptic curves defined over the field of rational numbers. Galois representations on ´etale cohomology play a central role in this field. The most remarkable aspects of this series of conferences is the omnipresent exchange between applied (codes, cryptography) and pure (arithmetic and geometry) mathematics. The first branch supplies the second with new problems. For example, the impulse of Serre, Manin, and Ihara, motivated by the introduction of Goppa codes, led to hundreds of articles devoted to the study of the number of points on curves over finite fields. A more specialized and recent example concerns quantum codes that lead to the study of couples code/sub-code having special properties. As a counterpart, arithmetic and geometry allow remarkable new results to be obtained in their applications. For example, cryptosystems constructed from elliptic curves over finite fields, or the best asymptotically excellent codes constructed using algebraic varieties.

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 conference will focus on the recent developments in arithmetic geometry, its applications and explicit and computational methods in approaching the relevant problems. There will be four main axes around which all talks will be organised: Automorphic forms and moduli spaces; Galois representations: geometric and constructive, modularity; Rational points and obstructions; Effective methods in arithmetic geometry. Leading experts in the field have accepted to contribute to the conference, making it a particularly interesting event.

The conference is dedicated to the memory of Bas Edixhoven (Professor, Leiden University)

This conference focuses on categorification and its applications in representation theory. Categorification is something of an art, where one mathematical object is replaced with another richer, and often categorical, one that often reveals deeper structual properties. Important examples of categorification in representation theory include the geometric categorifications of Ginzburg, Lusztig and Nakajima, which realize quantum groups and their representations in a geometric framework, and Khovanov's categorification of the Jones polynomial, and Elias and Williamson's proof of the Kazhdan-Lusztig positivity conjectures and Soergel's conjectures.

This conference brings some of the top experts in this field to discuss recent advances. The conference consists of:

A workshop, February 6-10, with three lecture series on different aspects of categorification The main conference, February 13-17.

Speakers:

• Prasit Bhattacharya, New Mexico State University
• Kalina Mincheva, Tulane University
• Peter Patzt, University of Oklahoma
• Maru Sarazola, Johns Hopkins University
• Shira Tanny, Institute for Advanced Study
• Melissa Zhang, UC Davis

The conference will be devoted to the study of algebraic varieties over finite fields from an algebraic geometry point of view as a combinatorial one and their applications to coding theory.

Featured topics will include theoretical, effective and algorithmic aspects of point counting as well as algebraic geometry codes constructed from curves and higher dimensional varieties.

This conference is devoted to the algebraic and combinatorial aspects of codes and cryptography and the links between codes and cryptography. It aims at gathering international experts, including researchers from the University of Aix-Marseille, in this essential and very active field of mathematics and theoretical computer science. This event aims also to provide a forum for researchers working on algebraic and combinatorial methods for coding and cryptography, exchange ideas and interests in open problems, and further explore their applications in cryptography error-correcting codes and communications. We plan to issue a ”Call for Paper” for specialized talks and select some presentations to be published in the congress proceedings in the international journal Advances in Mathematics of Communications édited by American Institute of Mathematical Sciences and handled by Jintai Ding and Sihem Mesnager as Editors-in-Chief.

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 main scientific theme of the workshop is counting BPS states in physical systems associated to 3-manifolds or links, and interpretation of these counts as old or new topological invariants.

Although the ideas behind such relations appeared already in the late 90s, the recent years have seen some dramatic new developments. The goal of this learning workshop is to bring together physicists and mathematicians who are experts in the subject and also those who would like to enter the field. In particular, the talks will be given both by senior scientists and junior ones, including PhD students who only recently began working on the subject. The talks will be supplemented by dedicated discussion sessions where experts can answer questions that will be submitted by participants to the moderator in advance, or asked directly during the session.

Topics:

-- "Z-hat" and F_K invariants counting BPS states in 6d superconformal field theory compactified on 3- manifolds, and their relation to known invariants of 3-manifolds and links

-- Knots-quivers correspondence and its generalization to knot complements

-- Properties of generating functions counting BPS states, including: modularity, relation to characters of (logarithmic) Vertex Operator Algebras, GW/DT invariants

To commemorate the 135th birth year of Srinivasa Ramanujan, IIT Kanpur, C3i Hub, VIBHA, and the Ministry of Culture, Government of India will be organising an event from 28 Feb to 01 Mar 2023 at IIT Kanpur in the broad theme of number theory, and its application in computational problems.

Some of the leading experts in the relevant areas will be present in this meeting to discuss their research work.

Young researchers including some PhD students will also be present in this event.

Speakers:

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

with Clay Lecturer: Boris Zilber

There is a history of fruitful links between low-dimensional topology and number theory, going back at least to Mazur's observation that primes in number rings can be viewed as analogues of knots in a 3-manifold. More recently, the introduction of arithmetic gauge theory by M. Kim and collaborators paves the way to further bring ideas from theoretical physics to bear on fundamental problems in number theory and arithmetic geometry. 

This conference aims to explore this exciting new direction, and the links between number theory, topology and physics in general, with a particular focus on the role played by gauge fields as a unifying framework. In doing this, we will bring together experts and early career researchers in each of the areas mentioned above, with a view to fostering new collaborations and enabling participants to become acquainted with recent developments.

Dear all,

this is the first announcement of a conference that we are organizing at the Max Planch Institute for Mathematics in Bonn, on "Motives and Automorphic Forms", in honour of Günter Harder's 85th Birthday, March 6 - 10, 2023.

The school will consist of three mini-courses by A. Raghuram (on Eisenstein cohomology), M. Levine (on motivic cohomology) and J. Wildeshaus (on intersection motives of Shimura varieties), along with several research talks. A more detailed description is available on the webpage https://www.mpim-bonn.mpg.de/node/11596. [1]

We encourage participants to seek external funding, so that the limited financial support available can be primarily used for early career mathematicians. In case you do need financial support, you can indicate this in the registration form in the above webpage.

If you would like to participate, please register before November 27, 2022 (we reserve the right to close the registration earlier, depending on demand). We especially welcome applications from members of minority groups. The total number of participants is limited

Looking forward to seeing you in Bonn, the organizers

Jitendra Bajpai, Mattia Cavicchi, Christian Kaiser and Peter Moree

Links:

[1] https://sites.google.com/view/motives-arithmeticgroups

Families of p-adic automorphic forms are well studied objects of arithmetic geometry since the pioneering work of Hida and Coleman. Their study resulted in the definition of geometric objects, called eigenvarieties, that parametrize systems of Hecke eigenvalues of p-adic automorphic forms. Conversely, the rich geometry of these varieties gives insights about p-adic (and thereby also about classical) automorphic forms. Recent techniques from perfectoid geometry, locally analytic representation theory and the point of view of the p-adic Langlands program give new insights and impulses.

The spring school will give an introduction to both p-adic automorphic forms and eigenvarieties as well as the necessary background in p-adic analytic geometry. The courses will be complemented by research talks that will focus on recent developments in the area.

The first week of the spring school will focus on p-adic analytic geometry, the analogue of complex analytic geometry over p-adic base fields. We will study classical rigid analytic spaces from the point of view of adic spaces and introduce perfectoid spaces. The second week will focus on p-adic automorphic forms and eigenvarieties. We will introduce and compare several approaches to p-adic automorphic forms.

Spring School lectures:

• John BERGDALL, University of Arkansas
• Eugen HELLMANN, University of Münster
• Ben HEUER, University Bonn
• Katharina HÜBNER, University of Heidelberg
• Adrian IOVITA, Univ. Concordia / Padua
• Christian JOHANSSON, University of Gothenburg
• Judith LUDWIG, University of Heidelberg
• James NEWTON, University of Oxford

Research Talks:

• Rebecca BELLOVIN, University of Glasgow
• Chris BIRKBECK, University College London
• Christian JOHANSSON, University of Gothenburg
• Lucas MANN, University Bonn
• Joaquín RODRIGUES JACINTO, Univ.Paris Saclay
• Mingjia ZHANG, University Bonn
• Vincent PILLONI, Université Paris-Saclay

A conference dedicated to the memory of Claus-Günther Schmidt.

Committee: Haruzo Hida (UCLA), Fabian Januszewski (Paderborn University), Tadashi Ochiai (Osaka University), A. Raghuram (Fordham University)

For details, please refer to the conference website.

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.

Welcome to the icebreaker event for Early Career Mathematicians (ECM) at the BAMC 2023, sponsored by the ECM Committee of the Institute of Mathematics and its Applications (IMA). We had a fantastic time last year at Loughborough, so much so that we are going to run the same event in Bristol. We are hosting the event at Design West, right in the city centre of Bristol, the evening before the BAMC begins.

Feedback we, the Committee, received from our members is that networking and forming contacts with others at conferences can be daunting. In the instances that a group of friends has been formed, they have said that the enjoyability of the conference improves significantly. So, forming contacts and groups is what we want to facilitate at this event. We will start the event with quick opening speeches about the BAMC (and ECMs) from one of the Organising Committee and who the ECM Committee are and what they do for the IMA. Then we will start the activities, which include: • Knowing me, knowing you • Mathematical Taboo • Celebrity Cameo • Mathematical Headbandz • Shakespeare's Radio

Refreshments will be supplied and you are welcome to join the ECM Committee for an informal dinner after the event.

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.

This workshop will bring together leading, as well as early career, researchers on arithmetic statistics and on algorithmic aspects of algebra and number theory, with the aim of fostering collaborations within and between these communities, and to offer early career researchers the opportunity to get a broad overview of the most recent achievements and of the most pressing problems in these fields. The workshop will also celebrate the mathematics of Hendrik W Lenstra Jr.

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 workshop Around Complex Geometry will take place at the University of Illinois at Chicago April 21-23 2022. The plan is to bring a mix of senior and junior researchers with interests in complex geometry and related fields.

The field of arithmetic statistics is a fast-moving area of number theory, dealing with distributional results for many basic and important objects: ranks of elliptic curves, central values of L-functions, number fields, modular symbols, orbits of discrete groups etc. The techniques involved come from diverse areas of mathematics e.g. automorphic forms, ergodic theory, spectral theory, dynamical systems, probabilistic number theory, representation theory and random matrix theory. This workshop intends to bring together researchers of all career levels to present their work and exchange ideas and techniques on arithmetic statistics. Motivated by the programme of Mazur and Rubin based on their computational study of elliptic curves over abelian extensions of fixed degree, the meeting will focus on modular symbols, Manin's noncommutative modular symbols, equidistribution of lattice points on the sphere, Heegner points, and closed geodesics, including the error term in the Prime Geodesic Theorem.

There will be invited talks lasting 50 or 25 minutes and other events aimed at facilitating discussions among participants.

Innovations and applications through the mathematics of operational research

Building on the success of the three previous conferences held in 2017, 2019, and 2021 this conference will aim to draw together the considerable community of researchers and practitioners who use/develop innovative mathematics, relevant to the applications and theory of Operational Research. The conference will showcase activities from across OR, and will welcome both contributions which have a clear application focus as well as those which are theoretically driven.

Contributions will be expected to showcase both Mathematics and OR. The conference will host plenaries from leading international experts, sessions of themed talks, as well as poster sessions, and provide plenty of opportunities for networking.

Invited Speakers Nira Chamberlain (SNC-Lavalin Group Inc) Joerg Fliege (University of Southampton) Paul Harper (Cardiff University) Julie Bennell (University of Leeds)

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

Speakers

• Ramla Abdellatif (Université de Picardie Jules Verne)
• Fabrizio Andreatta (Università di Milano)
• Kübra Benli (University of Georgia) TBC
• Francesco Campagna (Leibniz Universität Hannover)
• Cécile Dartyge (Université de Lorraine)
• Lassina Dembélé (King's College)
• Florent Jouve (Université de Bordeaux)
• Kamal Khuri-Makdisi (American University of Beirut)
• Myrto Mavraki (Harvard University) TBC
• Giovanni Rosso (Concordia University)
• Julia Wolf (University of Cambridge)
• Umberto Zannier (SNS Pisa)

In occasion of the seventh mini symposium it will be held, on May 2nd and 3rd, in Rome an atelier LEAN.
Attendance to the atelier LEAN is limited to 40 participants.

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 8th Lake Michigan Workshop on Combinatorics and Graph Theory will benefit graduate students and junior researchers in the field of discrete mathematics. It will be built around two sets of three tutorial lectures, focusing on state-of-the-art techniques and results that the speakers feel are underrepresented in typical graduate sequences, and on emerging techniques on which the speakers are particularly qualified to expound. There will also be short talks by students and younger faculty members, and a problem session. There will be ample unscheduled time during the weekend

The tutorial speakers for the 2023 workshop will be

• Will Perkins (Georgia Institute of Technology), who will speak on Statistical physics methods in combinatorics, and

• Stephanie van Willigenburg (University of British Columbia), who will speak on Coloring with a limited paintbox (the chromatic symmetric function).

Thanks to funding from NSF and Notre Dame, we anticipate supporting the travel and accommodation of junior participants, particularly those from the Midwest/Great Lakes/Great Plains area. More details will be available at the workshop website in early February.

The conference will focus on the areas of motivic and equivariant homotopy theory, K-theory. These topics have deep connections and applications to a wide variety of research areas, including algebraic geometry, topology, category theory and number theory. The aim of this conference is to share the latest developments and applications in these topics.

This workshop is being organized in celebration of Bhargav Bhatt’s Nemmers Prize.

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 is a 4-day conference in the areas of number theory and combinatorics. I will include four plenary talks and a number of contributed talks. Please see the website for more details. This will be the ninth Integers conference.

Over the last 35 years, the Annual Workshop on Automorphic Forms and Related Topics has remained a small and friendly conference. Those attending range from students to new PhD's to established researchers. For young researchers, the conference has provided support and encouragement. For accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas.

The workshop has become internationally recognized for both its high-quality research talks and its supportive atmosphere for junior researchers. Participants present cutting-edge research in all areas related to automorphic forms. These include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many other topics.

In addition to research talks, the workshop has, in the past years, featured panel discussion sessions on the topics of grant writing, mentoring and research partnerships, REUs and outreach, and opportunities for international collaborations. Based on the success of these sessions, we plan to have similar panel sessions this year as well.

Conference dedicated to the memory of Bas Edixhoven

A Conference in Honour of Mike Hopkins

The scientific program (13-15th June) is devoted to lectures given by the participants and invited lectures on various fields of Finsler geometry and applications to mathematical physics, and other fields.
See the Scientific Committee at : https://konferencia.unideb.hu/en/cfga-2023

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.

In the early 1920s, Emmy Noether introduced the fundamental concept of a Noetherian ring, a notion that has had a remarkably broad impact on mathematics over the last century. In this conference, we celebrate Noether's legacy with research talks from many areas of algebra, broadly construed, including algebraic geometry, commutative algebra, number theory, and representation theory.

This, the 16th in a series of Workshops in Alpbach, will feature minicourses given by world class researchers and invited talks by younger researchers, covering topics in arithmetic geometry related to Galois representations and heights. The emphasis includes not only deep theoretical developments, but also applications of a more concrete/computational nature. Minicourses presenting a broad overview of these topics, delivered by top international experts, will be complemented by invited talks highlighting recent progress.

Interest in specialization of polynomials and Galois groups goes back at least to the work of Hilbert on the inverse Galois problem. This theory has found an abundance of applications in Algebra, Number Theory, Group Theory, and Arithmetic Geometry. In recent years, the area is blooming and we see striking results that open completely new horizons: The discovery of Hilbert irreducibility properties of algebraic groups, its connection with expanders and random walks, the interrelation with arithmetic-geometric properties of parametrizing varieties, and the exciting progress on the Cohen-Lenstra heuristics. The conference aims to bring together leading experts and young researchers interested in the area. We plan to leave an abundance of free time, dedicated to informal discussions. We believe that this will encourage the transfer of ideas, techniques, and will foster new collaborations and new research directions.

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

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

It is the second edition of the series of conferences, under the title: Constructive Mathematics as a Bridge Between Classical Mathematics, Mathematical Education, Philosophy of Mathematics and Computer Sciences - An Appealing Intellectual Unification. This year’s conference will be dedicated to the memory of the American mathematician Errett Bishop celebrating the 95th ANNIVERSARY of his birth as well as the 55th anniversary of the publication of his seminal book Foundations of Constructive Analysis. The main aims of the conference are: to provide an opportunity for experts to present and discuss their recent research in seminars that relate to the various aspects and implications of constructive mathematics; to hold a mini-series of lectures, presented by experts in various fields and designed to engage academics from STEM disciplines and Humanities (including graduate students) in the discussions around the recent developments in constructive mathematics and its applications.

Thus, we call for an intriguing intellectual unification of different disciplines. The guiding questions behind the conference include: What happens when we free ourselves from the governing metaphors within our disciplines? Do we see commonalities across the disciplines in how that was/is done? Given this short synopsis of the ideas behind how we envision this conference and its contributions to the multidisciplinary landscape, we hope that the rich discussions during the conference and the publications that will be put out afterwards will constitute a significant contribution to the field and initiate new collaborations CM:FP 2023 conference is a result of collaboration between the following three academic groups/organizations: Center for Applied Mathematics of the Faculty of Mechanical Engineering Niš, CAM-FMEN, University of Niš, Serbia; Cognitive Science Network (Fields Institute for Research in Mathematical Sciences), Canada; International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, University of Abomey-Calavi, Benin.

The 2023 Summer School on Scissors Congruence, Algebraic K-theory, and Trace Methods for graduate students and early career researchers will be held June 26-30 at Indiana University, Bloomington.

The summer school will include mini-courses on:

• Algebraic K-theory - Mona Merling
• Scissors congruence K-theory - Inna Zakharevich
• Trace methods - Teena Gerhardt and Cary Malkiewich

The summer school will also feature problem sessions and student talks on foundational papers in the area.

We expect to provide housing for invited participants as well as (partial) reimbursement for travel expenses. We expect approximately 40-50 participants overall.

For more information, and to apply, please see: https://topology.math.indiana.edu/Summer2023/
Applications are due January 31st, 2023.

Organizing Committee:

• Andrew Blumberg
• Teena Gerhardt
• Michael Hill
• Cary Malkiewich
• Michael Mandell

• Andrew Blumberg, Columbia University
• Anna Marie Bohmann, Vanderbilt University
• Teena Gerhardt, Michigan State University
• Mike Hill, UCLA
• Cary Malkiewich, Binghamton University
• Michael Mandell, Indiana University
• Mona Merling, University of Pennsylvania
• Kate Ponto, University of Kentucky
• Inna Zakharevich, Cornell University

This workshop is organized around the themes of using refined invariants of algebraic varieties to study enumerative questions, with ideas coming from motivic homotopy theory, quadratic enumerative geometry, hermitian K-theory and beyond.

The Department of Mathematics of University of Patras and the Department of Electrical and Computer Engineering of University of Peloponnese with the hospitality of the city of Nafpaktos organize the:

"2023 International Conference on Topology and its Applications, July 3-7, 2023, Nafpaktos, Greece"

Organizing Committee: S. Iliadis - Chairman, D. Georgiou (Department of Mathematics, University of Patras, Patra, Greece), I. Kougias (Department of Electrical and Computer Engineering, University of Peloponnese, Patra, Greece), A. Megaritis (Department of Physics, University of Thessaly, Lamia, Greece), F. Sereti (Department of Mathematics, University of Western Macedonia, Kastoria, Greece), V. Gkizas (Mayor of the Municipality of Nafpaktia)

Host:
University of Patras - University of Peloponnese

Homepage:: http://www.lepantotopology.gr

e-mail: [email protected]

Description: All areas of Topology and its Applications are included: General Topology, Set-Theoretic Topology, Geometric Topology, Algebraic Topology, Applied Topology. In particular: Topological Groups, Dimension Theory, Dynamical Systems and Continua Theory, Computational Topology, History of Topology.

The above conference is the continuation of the following conferences:

(1) 2006 International Conference on Topology and its Applications,_ June 23-26, 2006, Aegion, Greece.

(2) 2010 International Conference on Topology and its Applications,_ June 26-30, 2010, Nafpaktos, Greece.

(3) 2014 International Conference on Topology and its Applications,_ June 3-7, 2014, Nafpaktos, Greece.

(4) 2018 International Conference on Topology and its Applications,_ July 3-7, 2018, Nafpaktos, Greece.

This event is the premier maintenance and reliability modelling conference in the UK and builds upon a very successful series of previous conferences. It is an excellent international forum for disseminating information on the state-of-the-art research, theories and practices in maintenance and reliability modelling and offers a platform for connecting researchers and practitioners from around the world. The scope of the conference includes: • Engineering Economy and Cost Analysis • Life cycle/performance analysis • Maintenance and Reliability Modelling • Prognostics and Health Management • Reliability and Maintenance Engineering • Safety, Security and Risk Management • Spare Parts Supply Chain Management • Warranty Management and Data Analysis • Machine learning for reliability engineering and maintenance optimization

Presentations are encouraged on the theory or application of maintenance and reliability for: • Autonomous Systems • Cyber-physical systems • Data Mining and Machine Learning • Decision Analysis and Methods • Human Factors • Information Processing and Engineering • Manufacturing Systems • Expert Elicitation • Operational Research • Production Planning and Control • Quality Control and Management • Resilience Engineering • Sustainability • Smart Technologies • Systems Modelling and Simulation

Keynote Speakers Prof Phil Scarf, Cardiff University
Prof David Coit, Rutgers school of engineering

This conference is organized around the themes of K-theory, (motivic) homotopy theory, topological Hochschild homology, trace methods, and related topics. It is dedicated to Bjørn Ian Dundas on the occasion of his 60th birthday.

Victor P. Snaith (1944 – 2021) was distinguished not just as an outstanding mathematician who made deep and lasting contributions in algebraic topology and number theory but also as a charismatic leader who enthusiastically developed research communities and generously supported young researchers.

The conference will bring together homotopy theory, cohomology of groups, algebraic K-theory and number theory, the main areas in which Vic worked. The aim is to feature important developments, paying special attention to synergies between these areas, as Vic did in much of his versatile research.

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.

The last few years have witnessed an explosion of progress in algebraic K-theory. Derived algebraic geometry and non-commutative methods have been refined into powerful tools, especially through the theory of localizing invariants. Trace methods have brought K-theory and topological cyclic homology closer together than ever before. Perfectoid techniques mean that K-theory benefits from the recent progress in p-adic cohomology, such as prismatic cohomology. Condensed mathematics provides at long last a uniform approach to the K-theory of topological rings. Geometric foundations for motivic stable homotopy theory have been laid and new motivic filtrations have been unearthed.

The goal of the Summer School will be to help bring the participants up to date on these exciting developments, via research lectures, mini-courses, and an Arbeitsgemeinschaft on the topic of syntomic and étale motivic cohomology.

Following the highly-successful first AGNES Summer School on higher dimensional moduli in 2022, this school will focus on intersection theory on moduli spaces. The past few years have seen spectacular progress in explicit computations of the cohomology and rational/integral Chow rings of moduli spaces of curves and related objects. This school will introduce graduate students to a range of techniques in this active area through four mini-courses. A key component of the school will be afternoon working sessions, where participants will work together in groups on problems, ranging from exercises to open-ended examples and research problems, relating to the topics of the lectures.

This summer school is designed for graduate students who have completed a yearlong course covering the foundations of algebraic geometry (e.g., Hartshorne's Algebraic Geometry) and are working in the field.

The minicourses will be given by Andrea di Lorenzo, Eric Larson, Hannah Larson, and Angelo Vistoli.

ICoMS 2023 is organized to bring together researchers and practitioners interested in advancing the state of the art in Mathematics and Statistics, and for exchanging knowledge that encompasses a broad range of disciplines among various distinct communities. The themes for this conference are focused on "Mathematics of Digital Twins - Analysis, Stochastics and Numerics". Conference Proceedings are published in ACM Digital Library, and there is a special Issue "Selected Papers from the 2023 6th International Conference on Mathematics and Statistics (ICoMS 2023)" in MDPI Mathematics.

This is the ninth Iwasawa conference following conferences in Besancon, Limoges, Irsee, Toronto, Heidelberg, London, Tokyo and Bordeaux. The conference is dedicated to the memory of John Henry Coates.

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.

The goal is to produce a collaborative environment for discussions of recent developments about spectral gaps, that bring together groups of researchers with different perspectives and backgrounds. All participants will be given fully catered accommodation at Collingwood College Durham

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.

This will be a workshop in arithmetic and algebraic geometry, similar to the previous iterations (in 2017 and online in 2020). The intended participant is a graduate student, or a postdoc, or even a senior researcher. You will work on a single topic, possibly related to the Stacks project, in a small group together with a mentor for a week. Part of this process will be seeing how one builds new theory from the foundations. There will also be one or two talks per day covering advanced topics in arithmetic or algebraic geometry.

The Stacks project workshop will have some optional activities you won't see at other workshops. Adding references to and finding mistakes in the Stacks Project (and fixing them) as well as activities related to LaTeX use, Git, and GitHub. Overall these will be aimed at helping you contribute efficiently to the Stacks project.

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.

There is growing demand, for scientific and evidence-based decision-making defence and security at the heart of government and in industry. Mathematics is fundamental to, providing a framework for understanding and solving varied and complex problems, and model system and scenarios. One of the biggest challenges for mathematicians is the ubiquity of the discipline- that the same maths can be used to solve multiple problems. It may not be obvious branch of mathematics best address a particular problem. Furthermore, finding a forum where you can get feedback on the different mathematical techniques that could be applied is not always straightforward.

The aim of the conference is to bring together researchers at the crossroads of algebra and number theory working on dynamic or asymptotic aspects.

CAIM series provide a forum for the review of the recent trends in applied and industrial mathematics either from a qualitative or from a numerical point of view.

The conference is about recent developments in Arithmetic Algebraic Geometry. Its central theme is the geometry of Shimura varieties and related spaces in all its facets. Topics to be covered include: Integral models of Shimura varieties and the geometry of their reductions, p-adic and perfectoid geometry, special cycles on Shimura varieties, moduli spaces of Galois representations and (φ, Γ)-modules.

This semester-long program in geometric analysis will focus mostly on complex geometry and Kähler geometry, but with the occasional excursion into real geometry. While the inspiration has deep geometrical roots, the tools are to a large degree those of partial differential equations. A lot of the activity will centre on six workshops:

PDEs in Complex Geometry (April 15-19, 2024)

Special Riemannian Metrics in Dimensions 6,7,8 (April 22-26, 2024)

Analysis of Geometric Singularities (May 13-17, 2024)

Moduli Spaces and Singularities (May 20-24, 2024)

Current Trends in Kähler Metrics with Special Curvature Properties (June 17-21, 2024)

Current Trends in Geometric Flows (June 25-29, 2024)

There will be a significant portion of the term and its resources devoted to training. Apart from resources set aside for students to attend the workshops, the semester will coordinate with the Séminaire de Mathématiques Supérieures (SMS). This school, a Montreal tradition, has been providing high-level training for graduate students since 1960, with some of the very top leaders in the field as lecturers.

We think that the 2024 SMS will be no exception. The topic is:

Flows and Variational Methods in Riemannian and Complex Geometry: Classical and Modern Methods (June 3-14, 2024).

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

See conference website

The aim of this meeting is to 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.

Because of limited space, participation is by invitation only.