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CIRM - Jean-Morlet Chair

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.

Mathematical Sciences Research Institute (MRSI)

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.

Mathematical Sciences Research Institute (MSRI)

This workshop is about the recent MIP*=RE result from quantum computational complexity, and the resulting resolution of the Connes embedding problem from the theory of von Neumann algebras. MIP*=RE connects the disparate areas of computational complexity theory, quantum information, operator algebras, and approximate representation theory. The techniques used in the proof of MIP*=RE, such as self-testing and probabilistically checkable proofs, are well-known in theoretical computer science and quantum information, but are unfortunately completely foreign in operator algebras and approximate representation theory. Likewise, the tools of operator algebras and approximate representation theory are mostly unfamiliar in theoretical computer science and quantum information. This has made it challenging to translate the MIP*=RE result and the techniques used to prove it into a form digestible to operator algebraists. The aim of this workshop is to bridge this divide, by giving an in-depth exposition of the techniques used in the proof of MIP*=RE, and highlighting perspectives on the MIP*=RE result from operator algebras and approximate representation theory. In particular, this workshop will highlight connections with group stability, something that has not been covered in previous workshops. In addition to increasing understanding of the MIP*=RE proof, we hope that this will open up further applications of the ideas behind MIP*=RE in operator algebras.

Mécanique quantique et l'information quantique,    Théorie de l'information quantique et informatique quantique

The conference is supported by the University of Pittsburgh Mathematics Research Center, and by the Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, is devoted to combinatorial problems about infinite cardinals. There are two types of infinite cardinals to investigate: successors of regular cardinals, most notably ℵ2, and successors of singular cardinals, for example ℵω+1ω+1. The workshop will focus on combinatorial principles such as the tree property, stationary reflection and the effect of consequences on forcing axioms on cardinal arithmetic, in particular what implications they have on the continuum, and the singular cardinal hypothesis (SCH).

The main topics of the workshop are The tree property, its strengthening ITP, stationary reflection how these combinatorial principles interact with SCH; Which consequences of PFA and MM require the continuum to be ℵ2 , and more generally, their effect on cardinal arithmetic; Forcing techniques such as proper iterated forcing and Prikry type forcing.

Ohio State University, Columbus

GPOTS focuses on recent advances in operator algebras (C* algebras, von Neumann algebras, and non-commutative geometry) and operator theory, with applications to a wide array of disciplines, including ergodic theory, representation theory, logic, and mathematical physics.

ICERM

In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology. This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.

Program Staff;     Tél.: [1-401-863-5030];     Email.: programstaff@icerm.brown.edu

Géométrie et topologie,    Analyse

Commutative Algebra has seen an extraordinary development in the last few years. Long standing conjectures have been proven and new connections to different areas of mathematics have been built.This summer graduate school will consist of three mini-courses (4 lectures each) on fundamental topics in commutative algebra that are not covered in the standard courses. Each course will be accompanied by problem sessions focused on research. Six general colloquium-style lectures will be given by invited scholars who will also attend the school and help with afternoon research activities.

University of Illinois Urbana-Champaign

Cours et évènements pour étudiants en mathématiques,    Théorie des graphes et combinatoire

Mathematical Sciences Research Institute (MSRI)

Computational proof assistants now make it possible to develop global, digital mathematical libraries with theorems that are fully checked by computer. This summer school will introduce students to the new technology and the ideas behind it, and will encourage them to think about the goals and benefits of formalized mathematics. Students will learn to use the Lean interactive proof assistant, and by the end of the session they will be in a position to formalize mathematics on their own, join the Lean community, and contribute to its mathematical library.

Cours et évènements pour étudiants en mathématiques,    Démonstration automatique de théorèmes

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.

Géométrie et topologie,    Théorie des nombres, arithmétique

Cours et évènements pour étudiants en mathématiques,    Géométrie et topologie

University of Oregon, Eugene

In this workshop we will explore the structure of these categorified Coulomb branches. The simplest (!) example of a categorified Coulomb branch is the coherent Satake category, that is, the category of perverse coherent sheaves on the affine Grassmannian of a complex reductive group (such as GL_n). This is the coherent analogue of the more classical (constructible) Satake category which plays a fundamental role in the geometric Langlands program. We don't expect participants to know what many of those words mean, but they will by the end of the workshop!

Cours et évènements pour étudiants en mathématiques,    Géométrie et topologie

Cours et évènements pour étudiants en mathématiques,    Géométrie et topologie

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will bring together theorists and computationalists to collaborate on understanding how computational considerations impact the practice of applied topology, and what new challenges for computation we must solve to bridge theory to applications.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the recent developments in the intersection of Khovanov-Rozansky homology, affine Springer fibers, Hilbert schemes and link homology, and combinatorics.

Géométrie et topologie,    Théorie des graphes et combinatoire

This will be a workshop in Algebraic Geometry, in topics (tangentially) related to the Stacks project. The participants who apply and are accepted will be graduate students, post-docs, or even senior researchers. Roughly the idea is that they will learn about and work on a single topic 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 some talks each day covering advanced topics in algebraic geometry. Mathematicians not in the groups are welcome to come to these talks.

Cours et évènements pour étudiants en mathématiques,    Géométrie et topologie

Mathematical Sciences Research Institute (MSRI)

The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field. It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

Mathematical Sciences Research Institute (MSRI)

This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

Mathematical Sciences Research Institute (MSRI)

Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field. This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

Mathematical Sciences Research Institute (MSRI)

This workshop will have a view to the future of a broad spectrum of topics including structure and classification of finite dimensional Lie algebras and superalgebras in characteristic p structure of infinite dimensional Lie algebras and their representations deformation theory of algebras, double constructions and elemental Lie algebras diagram algebras and combinatorial representation theory algebraic combinatorics of groups of Lie type:characters, Schur-Weyl duality, Bratteli diagrams, and McKay correspondences quantum groups and crystal bases, particularly for superalgebras and affine algebras examples of fusion categories arising from representations of Drinfeld doubles and other algebras cohomology for finite tensor categories with applications to its underlying geometry

This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

Massachusetts Institute of Technology (MIT)