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.

The study of rational points on varieties is a field of special interest to arithmetic geometers. Over the past few decades, many techniques have been used to decide whether a variety over a number field has a rational point or not, and even to describe those points completely. In this program, we are mainly interested in the study of rational points on modular curves.

Elliptic curves, modular forms and modular curves are central objects in arithmetic geometry. Modular curves can be thought of as moduli spaces for elliptic curves with extra level structures. The objective of this program is to understand the theoretical and computational aspects of determining K-rational points on modular curves X_H(K) for various fields K and subgroups H of GL_2(ℤ/Nℤ) for any natural number N.

In the mini-courses, we give an advanced introduction to the theory of rational points on modular curves, under both theoretical and computational aspects. These courses would include an introduction to the geometry of modular curves, their ℚ-rational points, classical and non-abelian Chabauty methods, and related computational aspects. We also attempt to strike a balance between the more advanced topics and the down-to-earth examples.

In the discussion meeting, we wish to bring many experts across the world in the area of arithmetic geometry together to share their ideas and the current state of research that will facilitate future research in this direction. We strongly encourage participation of young researchers.

There will be around 10 research minicourses on the subject of Geometry and Topology. Interested students should apply to the corresponding weeks from the website of the "Nesin Mathematics Village":

https://nesinkoyleri.org/en/events/2023-nmk-undergraduate-and-graduate-summer-camp/

Induction Course for New Lecturers in the Mathematical Sciences 2023 Monday 18th September- Tuesday 19th September 2023 9am-5pm Isaac Newton Institute for Mathematical Sciences, Cambridge https://ima.org.uk/22003/induction-course-for-new-lecturers-in-the-mathematical-sciences-2023/ Through a community initiative supported by the Institute of Mathematics and its Applications, the Isaac Newton Institute for Mathematical Sciences and the Heads of Departments of Mathematics Sciences (HoDoMS) and endorsed by the Royal Statistical Society, the London Mathematical Society, and the Edinburgh Mathematical Society, we are delighted to announce that in September 2023 the two‐day Induction Course for lecturers new to teaching mathematics and statistics within Higher Education will once again take place. The Induction Course is delivered as an in‐person only activity to maximise the opportunities for informal networking and discussion that have long formed a highly‐valued part of this meeting. The Induction Course for New Lecturers in the Mathematical Sciences has been designed by the mathematics community so that it is ideally suited for anyone who is new to or has limited experience teaching mathematics or statistics within UK higher education. It will be delivered by individuals with significant experience of teaching in the mathematical sciences and will focus upon the specific details and issues that arise in mathematics and statistics teaching and learning within higher education including topics such as: • Lecturing. • Supporting student learning. • Making teaching interactive. • Assessment, examinations and feedback. • Linking teaching & research. • Using technology to enhance teaching and learning. • Using examples and mathematical problem solving. • Teaching statistics and its applications. Additionally, there will be significant opportunities for delegates to discuss their own ideas, challenges and experiences with the session facilitators so that individual queries can be answered. In the past, attendance has been recognised as contributing towards some introductory institutional programmes in learning and teaching for new staff, and for the 2023 Induction Course accreditation will be provided through the Institute of Mathematics and its Applications relative to the UK Professional Standards Framework for Teaching and Supporting Learning in Higher Education. Session Facilitators Those leading the sessions at the Induction Course are all experienced teachers of mathematics within UK higher education. They include: • Lara Alcock (Loughborough University) • Michael Grove (University of Birmingham) • Rachel Hilliam (Open University) • Kevin Houston (University of Leeds) • Joseph Kyle (University of Birmingham) • Steve Otto (The R&A) • Chris Sangwin (The University of Edinburgh) • Louise Walker (The University of Manchester) • Ulrike Tillmann (Isaac Newton Institute for Mathematical Sciences) Induction Course Costs Following generous financial support from the Isaac Newton Institute for Mathematical Sciences, the Institute of Mathematics and its Applications and the Heads of Departments of Mathematical Sciences, we are able to offer the Induction Course at the following subsidised rates: Full residential delegate rate* (Both days including all lunches, refreshments, Course dinner and accommodation on 18 September) £299 Two‐day delegate rate (Both days including all lunches, refreshments, Course dinner but no accommodation) £240 Day delegate rate (including lunch and refreshments) £95 Induction Course dinner 18 September (as a separate purchase) £68 * Please note that accommodation is allocated on a first‐come‐first served basis Registration 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.

Contacts A full programme for the Induction Course will be released in August 2023, but for questions or queries about the academic content or structure of the Induction Course please contact: Michael Grove: [email protected] For general conference queries please contact: [email protected]

For further information or to register your interest, please contact the Conferences Department: Email: [email protected] Institute of Mathematics and its Applications, Catherine Richards House, 16 Nelson Street, Southend-on-Sea, Essex, SS1 1EF, UK

On the occasion of the 60th birthday of Tonghai Yang, we would like to bring together people from modular forms and arithmetic geometry to discuss recent advances in this conference.

The Institute of Mathematics and its Applications (IMA) is hosting its Employer’s forum at the University of Warwick on 20th September 2023 on the topic of “AI, automation and mathematics in supporting business decisions”. This will be an opportunity for businesses, including SMEs, to explore how AI and mathematics can impact business in the widest sense. There will be a keynote speaker and four further short presentations on topics ranging from automation of computer code to probabilistic modelling for decision making under uncertainty. There will also be poster presentations on a range of related topics and plenty of time for networking.

This event is FREE to attend.

Call for posters: Calling all departments of Mathematics, Statistics, Computer science – you are invited to submit posters on topics related to mathematical sciences in industry, including algorithms, ethics, natural language processing, computer vision, sustainability, automation, mathematical biology, decision support etc. Accepted poster presenters will be given the opportunity to give a 3-minute spoken promotion of their poster content.

This is a hands‐on workshop and will introduce delegates to the freely available, open‐source and general‐purpose programming language Python ‐ which is one of the most popular programming languages in the world. Python will be used to enhance the teaching and learning of Mathematics at A‐Level and beyond. Delegates need no prior knowledge of programming to benefit from this workshop.

Feedback from 2022 Workshops “Really enjoyed the session. Definitely inspired me to get into doing some Python programming (never used it before although used other languages) and applying this to mathematics problems” “A thoroughly informative and enjoyable course!” “Really good workshop; would love a follow-up workshop to increase the level of challenge.” “Stephen was very clear and knowledgeable” “Looking forward to the TensorFlow workshop in June.” “Thank you very much to Stephen and IMA for organising.”

Workshop Itinerary Friday 22 September 2023 12:00pm – 1:00pm Introduction and using Python as a powerful graphing calculator 1:00pm – 1:15pm Coffee Break 1:15pm – 2:00pm Symbolic Python with sympy 2:00pm – 2:30pm Lunch Break 2:30pm – 3:30pm Numerical Python and plots using numpy and matplotlib 3:30pm – 3:45pm Coffee Break 3:45pm – 5:00pm Programming, Jupyter notebooks, Google Colab and Beyond A‐Level Maths

Saturday 23 September 2023 10:00am – 11:00am Introduction and using Python as a powerful graphing calculator 11:00am – 11:15am Coffee Break 11:15am – 12:00pm Symbolic Python with sympy 12:00pm – 12:30pm Lunch Break 12:30pm – 1:30pm Numerical Python and plots using numpy and matplotlib 1:30pm – 1:45pm Coffee Break 1:45pm – 3:00pm Programming, Jupyter notebooks, Google Colab and Beyond A‐Level Maths Requirements Delegates need to download Anaconda on to their own computers: https://www.anaconda.com For Google Colab: https://colab.research.google.com/ delegates will need a Google account.

Registration for this event is open via the https://my.ima.org.uk/services.php?section=events Portal. This event costs £10 to book. Please note that the content for each workshop day is the same so please only book for one date. Registration will close on 20 September 2023. All joining information will be sent 24 hours prior to the event.

New Python Book The first section of my new book includes a gentle introduction to Python and Python for A-Level Maths! New Python Book – https://www.routledge.com/Python-for-Scientific-Computing-and-Artificial-Intelligence/Lynch/p/book/9781032258713# Additional Resources Python for employability: https://www.mathscareers.org.uk/python-for-a-level-maths-undergraduate-maths-and-employability/ Jupyter notebook covering the A‐Level syllabus: https://drstephenlynch.github.io/webpages/Python_for_A_Level_Mathematics_and_Beyond.html Beyond A‐Level Maths: https://drstephenlynch.github.io/webpages/DSAP_Jupyter_Notebook.html Organisers This event has been organised by Dr Stephen Lynch National Teaching Fellow FIMA SFHEA Inventor of binary oscillator computing Author of PYTHON, MATLAB®, MAPLE™ AND MATHEMATICA® BOOKS STEM Ambassador and Speaker for Schools MMU Public Engagement Champion.

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

The 2023 fall edition of the Midwest Topology Seminar

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.

The African Institute for Mathematical Sciences (AIMS), British Society for the History of Mathematics (BSHM), ICTP-East African Institute for Fundamental Research (ICTP-EAIFR), Institute of Mathematics and its Applications (IMA), International Centre for Mathematical Sciences (ICMS), Isaac Newton Institute (INI), London Mathematical Society (LMS) and Mathematical Association (MA) are holding a two day conference on Black Heroes of Mathematics. The Vision of the conference is ‘To celebrate the inspirational contributions of black role models to the field of Mathematics and Mathematics Education’. There will be a balance of technical talks by internationally renowned black speakers that include some detail of career paths and experience to provide a testimonial dimension. We plan to achieve a balance of career stage and gender. Organising committee Nira Chamberlain, IMA Alex Liu, ICMS Troy Astarte, BSHM Maya Everson, IMA Elizabeth Fisher, LMS Tanniemola Liverpool, University of Bristol Christie Marr, Isaac Newton Institute Chris Pritchard, MA Angela Tabiri, AIMS Katherine Wright, LMS Frank Neumann, LMS Registration is now open via https://www.icms.org.uk/events/2023/black-heroes-mathematics-conference-2023 and is free to attend

The goal of the FRNTD is to provide a venue for faculty, graduate students, and undergraduates on the Front Range who are interested in number theory to meet, learn, and collaborate.

For more information and to register, please visit our website: https://sites.google.com/colorado.edu/front-range-number-theory-day/home. If you would like to give a five-minute talk, please include your title on the registration form.

Weekend regional conference in number theory and arithmetic geometry, featuring two mini-courses and additional research lectures.

A highly focused workshop on recent developments in Brauer groups and derived categories, suitable for people working in the field, organized around a mini-course by each speaker.

The South Central Topology Conference III will take place at New Mexico State University in Las Cruces, NM, October 28 - 29, 2023. This event will feature talks by:

• Christin Bibby, Louisiana State University
• Christy Hazel, Grinnell College
• Neil Hofffman, Oklahoma State University
• Morgan Opie, University of California at Los Angeles
• Katherine Raoux, University of Arkansas
• Noelle Sawyer, Southwestern University

along with a math rodeo for graduate students and early-career participants to share their work in 12-minute talks. We have NSF support for travel and lodging. We ask participants to register and seek funding by September 15, 2023.

The conference will be preceded by an NMSU special colloquium series (October 27) featuring Agnes Beaudry (University of Colorado Boulder), Kate Poirier (New York City College of Technology), and Zhouli Xu (University of California at San Diego). For more information and the registration form, please visit the conference website.

This workshop is targeted towards late stage postdocs and early career faculty who are planning to (or already are) advising graduate students and postdocs. The workshop will bring together these junior researchers with experienced faculty mentors to discuss the many components of advising at the graduate and postdoctoral level. The workshop will feature panel discussion, small breakout sessions, and practice scenarios.

Please apply to attend the workshop at the website: https://sites.google.com/view/minms/home The deadline to apply is September 1st.

Thanks to funding from the NSF, we anticipate being able to fund the participation of most accepted participants.

Rice University will be hosting the Fall 2023 edition of the Texas Geometry and Topology conference from November 10th to 12th. Registration is now open at the conference website: https://sites.google.com/view/tgtc-fall-2023/home

The speakers are:
Steven Boyer (UQAM - CIRGET)
Aaron Calderon (U Chicago)
Daniel Groves (U Illinois, Chicago)
Jonathan Johnson (Oklahoma State U)
Giuseppe Martone (Sam Houston State U)
Maggie Miller (Stanford/U Texas, Austin)
Anna Parlak (U California, Davis)
Rachel Skipper (U Utah)
Jing Tao (U Oklahoma)
Bena Tshishku (Brown U)

Some funding for travel and accommodation is available with priority for graduate students and recent PhDs. The deadline to apply for funding is August 25th.

We hope to see you there!

The sixteenth annual Binghamton University Graduate Combinatorics, Algebra and Topology Conference (BUGCAT Conference) will be held in-person on November 11-12 at Binghamton University. Graduate students of all levels, as well as faculty, are invited to give a 20 minute talk; talks may be expository or on current research. We have three keynote speakers this year: 1. Teena Gerhardt, Michigan State University 2. Karl Lorenson, Penn State Altoona 3. Isabel Vogt, Brown University For more details, check the website: http://seminars.math.binghamton.edu/BUGCAT/index.html Deadlines for registration and submitting talks are October 18th. Deadline for requesting funding is September 30th. If you have any questions, please email [email protected]. We look forward to seeing you!

Fall workshop for the IAS special year on p-adic arithmetic geometry in 2023--2024. Registration form on website.

This is the first meeting of the Arithmetica Transalpina, a joint Number Theory seminar between ETH Zürich, FernUni Schweiz and the universities of Milan, Padova and Genova.

Magma is a world-leading computer algebra system developed by the Computational Algebra Group at the University of Sydney. It supports cutting-edge computations in algebra, number theory, algebraic geometry, and algebraic combinatorics and is used on a daily basis by thousands of research mathematicians in over 70 countries.

The group is led by Professor John Cannon, the founder of Magma, and of its predecessor Cayley. A world expert on the development and implementation of algorithms for mathematics, John's scientific contributions are recognised via many awards including the CSIRO Medal (1993); the ATSE Clunies Ross Award (2001); the Richard D. Jenks Memorial Prize (2006); and his election in 2022 as Fellow of the Australian Academy of Science.

This meeting brings together a group of leading international researchers who have many connections to both John and the broad subject areas. We will celebrate two events: the 30th anniversary of the official launch of Magma, and the outstanding contributions of John as he reaches a personal milestone.

The main conference , 27-29 November 2023
A workshop on Computational Number Theory , 30 November - 1 December 2023

Please register if you would like to attend the conference.

The Second International Workshop on Applied Mathematics (2nd-IWAM'2023) is one of the important activities of department of mathematics in the university ''FMC 1''. Its main goal is to promote the exchange and dissemination of the latest research advances in Mathematics developed by researchers from Algeria and abroad. In this 1st edition of the 2nd-IWAM'2023, lectures in different areas of Mathematics will be offered, including Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19), modelling in biology, medicine, chemistry, physics, Bioinformatics, Mathematical biology, Algebra, Numerical Analysis, Functional Analysis, Dynamics and Lie Theory, Geometry, Mathematics Education, Mechanics, Number Theory, Probability and Theory of Computation, programming languages, matrices to compiled languages. Maple, C et C++, MATLAB®, Java, JavaScript, Logiciel R, Python, R, Visual Basic, and Fortran. Statistical software (SAS, SPSS, Excel, R ). The conference provides participants with diverse perspectives on recent developments in mathematical science research. The event will be totally in the campus 'A. Hamani', UFMC 1, Department of Mathematics.The objective of this event is to bring together researchers and professionals working on applied mathematics themes in order to share their experiences and results and enrich the debate.

The mathematical theory and practice of both cryptography and coding underpins the provision of effective security and reliability for data communication, processing and storage. This nineteenth International Conference in an established and successful IMA series on the theme of “Cryptography and Coding” solicits original research papers on all technical aspects of cryptography and coding. Submissions are welcome on any cryptographic or coding-theoretic topic including, but not limited to: • Foundational theory and mathematics; • The design, proposal, and analysis of cryptographic or coding primitives and protocols • Secure implementation and optimisation in hardware or software; and • Applied aspects of cryptography and coding. Call for Papers The proceedings will be published in Springer’s Lecture Notes in Computer Science series, and will be available at the conference. Submissions must not substantially duplicate work that any of the authors has published elsewhere or has submitted in parallel to a journal or any other conference or workshop with proceedings. Accepted submissions may not appear in any other conference or workshop that has proceedings. Authors of accepted papers must guarantee that their paper will be presented at the conference and must make a full version of their paper available online. All submissions will be blind-reviewed. Papers must be anonymous, with no author names, affiliations, acknowledgements, or obvious references. Submissions should begin with a cover page containing title, a short abstract, and a list of keywords. The body of the paper should be at most 14 pages, excluding the title page with abstract, the bibliography, and clearly marked appendices. Committee members are not required to review appendices, so the paper should be intelligible and self-contained within this length. The submission must be in Springer’s LNCS format (LaTeX). Submissions not meeting these guidelines risk rejection without consideration of their merits. Submissions should be submitted via https://easychair.org/account/signin?l=wkSzSmtr1OTY2v9Kuv3Kft
Important Dates Submission Deadline: 28 June 2023 Author Notification: 6 September 2023 Proceedings Version Deadline: 20 September 2023

Organising Committee Elizabeth Quaglia, RHUL (Chair) Angelo De Caro, IBM Maura Paterson, Birkbeck Chris Mitchell, RHUL

Higher Dimensional Algebraic Geometry: James 60 is a conference highlighting recent progress in higher-dimensional algebraic geometry scheduled in honor of James McKernan's 60th birthday. The conference will focus on the many areas of algebraic geometry impacted by the groundbreaking work of James and his collaborators.

This workshop is mainly devoted to recent developments in Fourier analysis and function spaces. The aim is to represent a wide class of recent developments of the field, such as harmonic analysis on LCA groups, applications of positive definite functions, function spaces and inequalities, Riesz bases, etc.

Courses:

 Valentijn Karemaker: TBA
 Ben Moonen: TBA
 Rachel Pries: TBA
 Joe Silverman: TBA

With Clay lecturer Barry Mazur

This workshop, sponsored by AIM and the NSF, will be devoted to the study of degree d points on algebraic surfaces over a number field.

The study of degree d points on algebraic curves over ℚ is a rich and mature area of research, with the Abel-Jacobi map and the Mordell-Lang conjecture providing powerful tools for exploration. However, for higher dimensional varieties there is no such approach that works in general. Because of this, we lack even a conjectural framework for understanding which higher dimensional varieties over ℚ should have "many" degree d points.

The workshop will focus on questions aimed at addressing this dearth, concentrating on the case of algebraic surfaces. For instance, what does it mean for a surface over ℚ to have "many" degree d points? What are some geometric constructions that give rise to abundant degree d points? Are these related to geometric measures of irrationality? If HilbdX has a Zariski dense set of ℚ-points for some small d, does that yield any arithmetic or geometric consequences for X? If X embeds into its Albanese, can we obtain results analogous to that of curves?

Participants will be researchers from a broad array of backgrounds (e.g., arithmetic of surfaces, geometry of Hilbert schemes of surfaces, geometric measures of irrationality, arithmetic of 0-cycles, to name a few), ideally with a curiosity and interest in arithmetic questions.

This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

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).

In the 1980s, Ceresa exhibited one of the first naturally occurring examples of an algebraic cycle, the Ceresa cycle, that is in general homologically trivial but algebraically nontrivial. In the last few years, there has been a renewed interest in the Ceresa cycle, and other cycle classes associated to curves over arithmetically interesting fields, and their interactions with analytic, combinatorial, and arithmetic properties of those curves. We hope to capitalize on this momentum to bring together different communities of arithmetic geometers to fully explore explicit computations around the arithmetic and geometry of cycles, when these various approaches are systematically combined.

The summer school is dedicated to graduate students and young researchers, and aims to give an introduction to recent techniques and topics of additive combinatorics. The lectures of the summer school will concentrate on recent developments of the polynomial method, some combinatorial methods of additive combinatorics, and the introduction of Fourier analytic techniques connected to them. The main topics will be presented by top researchers of the area.

The lecturers will be Julia Wolf, Christian Elsholtz, Peter Pal Pach, Sean Prendiville.

The EPIGA 2024 conference will feature a series of lectures covering a large spectrum of algebraic geometry. Half a day will be devoted to talks and debates on the topic of scientific publishing. It will also be the occasion to award the first Demailly prize for open science.

This conference is devoted to the most recent results of Additive Combinatorics. The topic of the conference is aimed to emphasize the rich interactions between additive combinatorics, harmonic analysis and number theory. The conference will bring together some recognized experts of the field, junior researchers (postdoctoral fellows and graduate students), and senior researchers from various aspects of the main topic. Beside the discussion on the recent progress in the field, it is also aimed to initiate interaction and collaboration among the participants.

See conference website

After the success and impact of Spec(Q⎯⎯⎯⎯), held at the Fields Institute in 2022, Spec(Q¯(2πi)) again aims to celebrate and promote research advances of LGBTQ2I (Lesbian, Gay, Bisexual, Transgender, Queer, 2-spirit , Intersex) mathematicians specialising in algebraic geometry, arithmetic geometry, commutative algebra, and number theory. The first edition of the conference proved to be extremely important to lay the foundations for a fertile, supportive and stimulating scientific queer community in the areas of algebraic geometry, commutative algebra and number theory. Building on the strengths of the first edition, Spec(Q¯(2πi)) will create an empowering and engaging environment which provides LGBTQ2I visibility in algebraic geometry, will support junior LGBTQ2I 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 topics in 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¯(2πi)) will be aimed at a general algebro-geometric audience.

Algebraic geometry is the field of mathematics which concerns the study of spaces cut out by polynomial equations. This workshop concern the interaction of two important objects in algebraic geometry - the K-groups and the Brauer group. In algebraic geometry, we study spaces via invariants - the procedure of attaching simpler, more "linear" objects to these spaces in the hope of extracting information about them. Both the K-groups and Brauer group are such examples which have had an excellent track record in being both powerful and accessible at the same time. Roughly speaking, the K-groups are built out from \emph{vector bundles} on such a space - a continuous assignment of vector spaces on each point of the space. On the other hand the Brauer groups are built from "twisted" vector bundles.

Both invariants have had a history of interaction and cross-pollination and the goal of the workshop is to bring together researchers in both areas to share their research and pave the way for even more fruitful interaction in the future. We are particularly excited about the prospect of new, field-driving questions to come out from this workshop.

Hilbert’s twelfth problem asks for explicit constructions of the abelian extensions of a given number field, similar to what is known for the rational numbers and for imaginary quadratic fields. These abelian extensions are known as class fields because their Galois groups are identified with certain generalized ideal class groups. In the two known cases, the class fields are obtained via the adjunction of roots of unity and of torsion points on elliptic curves with complex multiplication. These are special values of complex analytic functions – the exponential function and elliptic functions with complex multiplication. Hilbert may have envisioned the use of special values of complex analytic functions to construct class fields of more general base fields.

In the 1970s, Harold Stark proposed a strikingly original approach to the generation of class fields, based on his conjectures on the leading term of Artin L-functions at s = 0 [St75]. In the case of abelian L-functions with a simple zero at s = 0, Stark predicted that the first derivative was the logarithm of a unit in the respective class field [St76], so exponentiating this derivative would give a generator for the abelian extension. In the two known cases, this reduced to the theory of circular and elliptic units, thanks to Dirichlet’s analytic class number formula and Kronecker’s limit formula. Although there is now extensive computational evidence that Stark’s conjecture is correct, there has been little progress on its solution.

In the 1980s Benedict Gross formulated some p-adic [Gr82] and tame [Gr88] analogues of Stark’s conjectures, which gave more information on the p-adic expansions of the conjectural units. Since the p adic L-functions involved in Gross’s conjecture are related to certain Galois modules via the main conjecture in Iwasawa theory, these conjectures have proved more amenable than their complex analogs. Refinements of the Gross-Stark conjecture were proposed in [DD06], and the p-adic conjectures of [Gr82] was proved in [DDP11]. This line of argument has culminated in the recent work of Samit Dasgupta and Mahesh Kakde [DKa], [DKb] which, by proving a large part of the conjectures of [Gr88] (along with the refinement [DD06] of the conjectures of [Gr82] in the broader setting of totally real fields) leads to a p−adic solution to Hilbert’s twelfth problem for this large class of fields.

The goal of this workshop is to take stock of this striking recent development and of other progress around the theme of related approaches to explicit class field theory. The key to much of the progress over the years is the careful study of p-adic and tame deformations of modular forms, most notably, of Hilbert modular Eisenstein series. The p-adic interpolation of classical Eisenstein series was introduced by Jean-Pierre Serre [Se72] to study the congruences of special values of L-functions and the construction of p-adic L-functions for totally real fields, and was further developed by Barry Mazur and Andrew Wiles in their proof of the main conjecture of Iwasawa theory [MW84]. The workshop will focus on the breakthroughs in [DKa] and [DKb], with a lecture series by the two authors forming the cornerstone of the activity.

In 2024, Péter Frankl, Zoltán Füredi, Ervin Győri and János Pach will turn 70. On the occasion of this joyful event, we organize a conference Sum(m)it280. We would like to invite you to celebrate these four Hungarian combinatorialists with us.

In the last few years, there have been extraordinary developments in many aspects of curve theory. Beginning with many examples in low genus, this summer school will introduce the participants to the background behind these developments in the following areas:

1. moduli spaces of stable curves
2. Brill–Noether theory
3. the extrinsic geometry of the curves in projective space

We will also include an introduction to some open problems at the forefront of these active areas.

School Structure

There will be two one-hour lectures and two problem sessions each day.

Prerequisites

Basic knowledge of algebraic geometry up to the level of the Riemann–Roch and Riemann–Hurwitz theorems for curves. (These theorems appear, for example, in Hartshorne’s Algebraic Geometry as Theorem IV.1.3 and Corollary IV.2.4; or in Sections 2.3 and 2.1 in Griffiths–Harris Principles of Algebraic Geometry).

Application Procedure

For eligibility and how to apply, see the main summer school page.

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.

In 2019, the organizers created a workshop called Number Theory in the Americas, which brought together junior and senior mathematicians from North, Central, and South America, to work together on research projects. The workshop resulted in at least seven publications, and served as a first collaboration experience for many of the junior researchers. The organizers propose to create a follow-up workshop in order to provide collaboration opportunities for the PhD students and postdocs who were too young to participate the last time. The workshop will be held in Spanish in order to erase the additional obstacle of communicating in English. We will welcome native and non-native speakers alike.

Our workshop is modeled after several other workshops that have been successful at fostering mathematical collaboration. Participants will be divided into small project groups (3-5 participants) containing a mix of junior and senior researchers. Each group will be led by one or two senior mathematicians. Project groups will be assigned based on research area, with care taken to ensure that each group contains researchers from both continents who have not previously worked together. Background reading will be sent to project group members several months in advance so that they are prepared to work on their respective problems together when they arrive in Oaxaca. The bulk of the workshop will be devoted to working in the project groups, but there will be introductory talks on the first day and final reports on the last day. There will also be panel discussions on topics of particular interest to junior researchers. The expectation is not that each project group will write a paper by the end of the week. Rather, it is meant to be an opportunity to exchange ideas and a starting point for potential future collaboration.

The conference "Number Theory, Quantum Chaos and their Interfaces” aims at gathering distinguished researchers working in either of the disciplines to discuss recent research advances in these fields, and serve as a playground for the exchange of ideas between these, rather diverse, research communities. Another purpose of our conference is to provide a solid educational platform for more junior researchers who aspire to conduct research in the relevant fields and expose them to some of the outstanding results and open problems.

The René 25 conference's purpose is to celebrate the research interests of René Schoof.

During the 2025-26 academic year the School will have a special program on Arithmetic Geometry, Hodge Theory, and O-minimality. Jacob Tsimerman, University of Toronto will be the Distinguished Visiting Professor.

The purpose of this special year will focus on recent developments in hodge theory and o-minimality and their applications to arithmetic geometry. There has been much progress over the last 15 years in using transcendental uniformization maps to study arithmetic questions (general shafarevich theorems, results on unlikely intersections, general bounds on rational point counts). It has become increasingly clear that hodge theory (both classical and P-adic) and the resulting period maps form a natural home for these kinds of investigations to arise. In the other direction, O-minimality has been applied with success to make progress on questions in Hodge theory (Griffiths conjecture, definable period maps), and has recently had its own explosion of results (sharply O-minimal sets, the resolution of Wilkie's conjecture).

The goal of this year will be to bring together researchers in these different fields, with the aim of extending the collaboration between areas, share key insights, and investigate how far existing methods can be pushed.

Senior participants: Gal Binaymini, Ben Bakker (to be confirmed), Jonathan Pila and Claire Voisin (STV)