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Institute for Computational and Experimental Research in Mathematics (ICERM)

Given an incidence structure, one may model a variety of geometric problems. This Semester Program will revolve around two fundamental examples and their applications to modern challenges in the study, analysis, and design of materials. (1) Packings and patterns of circles where the underlying combinatorics are mixed with advanced geometric concepts and strong links are made to discrete differential geometry. (2) The rigidity and flexibility of bar-joint structures where real algebraic geometry is intertwined with sparse graph theory and matroidal techniques. A prime objective of the program is to advance the applicability of these topics to fundamental applications, most notably in statistical physics and materials science.

The program will integrate diverse fields of discrete mathematics, geometry, theoretical computer science, mathematical biology, and statistical and soft matter physics. Various workshops will be designed to attract both theoretical and applied practitioners and to stimulate the cross-fertilization of ideas between these disparate communities.

ICERM;     Email: info@icerm.brown.edu

Metallurgie und Werkstoffkunde,    Thermodynamik, Hydrodynamik und Statistische Mechanik

Please join us to celebrate Stephan Stolz' retirement and topology and geometry in the Midwest!

Institute for Computational and Experimental Research in Mathematics (ICERM)

This workshop will be centered on recent advances in graph rigidity and interactions between rigidity, algebraic statistics, and matroid theory. Three major advances are the recent resolution of the matroid maximality conjecture, the newly developed link to maximum likelihood estimation in Gaussian graphical models, and the recent positive resolution of Lovasz and Yemini's connectivity conjecture for generic rigidity. The workshop will showcase a diverse sample of current work addressing fundamental problems in graph rigidity, algebraic matroids, and algebraic statistics.

ICERM;     Email: info@icerm.brown.edu

Celebrating Nick Kuhn's 70th birthday!

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to investigating new research directions within G2 geometry. Certain topics have by now been intensely studied: the construction of new holonomy G2 manifolds, submanifold geometry, gauge theory, geometric invariants and geometric flows. Across the years, however, many other promising directions have been suggested but await deeper investigation.

New developments in G2 mirror symmetry. Topological methods and formality in G2 geometry. Loop spaces and non-associative gauge theory. G2 function theory and G2 mappings.

Institute for Computational and Experimental Research in Mathematics (ICERM)

The geometric arrangement of a material’s constituents plays an important role in governing its behavior. Concepts from discrete mathematics to describe these geometric arrangements, including notions of rigidity and flexibility, can bring fundamental insight into how a material might respond to stress, be designed, be reconfigured, etc. Beyond materials, the notions of network rigidity can be applied to more abstract networks and geometries, such as those found in data science. This workshop aims to build connections between the field of mathematical rigidity theory, other topics in applied mathematics, and related areas of science and engineering.

ICERM;     Email: info@icerm.brown.edu

Graphentheorie und Kombinatorik,    Chemikalien und Materialwissenschaft

American Institute of Mathematics, Pasadena, California (AIM)

This workshop will bring together low-dimensional topologists of all backgrounds to further the general knowledge of link theory within the low-dimensional topology community, including techniques and tools used to study links and important open questions connected to link theory. In particular, the workshop will highlight how computation interacts with current research in link theory. The workshop will also provide a space for new collaborations to develop and promote a supportive and inclusive environment within the community of researchers.

University of Georgia

The 2025 Georgia International Topology Conference https://topology.franklinresearch.uga.edu/2025GITC will take place May 19 - May 30, 2025 at the University of Georgia in Athens, Georgia. This will be the ninth in a series of octennial conferences at the University of Georgia that started in 1961.

University of Notre Dame

This summer school will focus on focus on Legendrian links and the microlocal theory of sheaves and run from June 9th through June 13th, 2025. The summer school will be centered around a mini-course given by Roger Casals (the University of California, Davis). The mini-course will be supplemented by a couple of research talks, opportunities for participants to ask questions and work on problem sets, panel discussions about career paths, and a discussion of open problems.

University of Notre Dame

Gruppentheorie,    Zahlentheorie, Arithmetik

In recent years, there has been an explosion of activity surrounding algebraic points on curves, from many different perspectives. These include the study of measures of irrationality, isolated and parametrized points, computational methods to determine algebraic points, and the arithmetic statistics of algebraic points. In this workshop, we aim to bring together researchers from these diverse perspectives, with the particular goal of developing bridges between them. The workshop will include overview talks on the various perspectives, research talks, an open problem session, and structured time for collaboration.

Zahlentheorie, Arithmetik,    Algebra

University Texas at Austin

Join us for a five-day workshop hosted by UT Austin, with support from the NSF. Mornings will be dedicated to talks, and in the afternoons, participants will work in small groups on open problems related to connections between 4-manifold trisections and diffeomorphism groups. The workshop will be preceded by introductory mini-courses on Zoom taking place on June 18 and June 20. Participants may register for either or both workshop components. The workshop will conclude at noon on Friday, 6/27.

Email: zupan@unl.edu

4-manifold, trisection, diffeomorphism group, group action

Society for Industrial and Applied Mathematics (SIAM)

The purpose of the SIAM Activity Group on Algebraic Geometry is to bring together researchers who use algebraic geometry in industrial and applied mathematics. "Algebraic geometry" is interpreted broadly to include at least: algebraic geometry, commutative algebra, noncommutative algebra, symbolic and numeric computation, algebraic and geometric combinatorics, representation theory, and algebraic topology. These methods have already seen applications in: biology, coding theory, cryptography, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear partial differential equations, optimization, robotics, and statistics. We welcome participation from everyone interested in this broadly interpreted notion of algebraic geometry and its applications.

Algebra,    Angewandte Mathematik (allgem.)

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM, the NSF, and the Merkin Center at Caltech, will be devoted to the theory of metric embeddings and its interactions with geometry, analysis, probability, combinatorics, group theory, topology, and theoretical computer science. It will provide the opportunity for researchers to learn about major recent advances in this area. Another goal of the conference is to revive Matoušek’s influential list of "Open Problems on Embeddings of Finite Metric Spaces" (https://kam.mff.cuni.cz/~matousek/metrop.ps), by updating it to reflect progress on existing problems, and adding to it a list of new questions and challenges.

Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups. These subgroups are central objects in the study of higher Teichmuller theory, convex projective geometry, and character varieties. In this summer school, there will be an emphasis on discussing some of the dynamical tools that have recently been successfully used to study Anosov subgroups. The required background in dynamics, hyperbolic geometry, and Lie theory will also be discussed. Aside from providing a stimulating academic environment for learning about Anosov subgroups, this summer school also aims to be a relaxed and friendly space for participants to interact with fellow aspiring mathematicians.

Gruppentheorie,    Kurse und Veranstaltungen für Studenten der Mathematik

Organised in partnership with the Clay Mathematics Institute

Simons Laufer Mathematical Sciences Institute (SLMath)

This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in Low-Dimensions”. The school consists of two mini-courses: one on Teichmüller Theory and Hyperbolic 3-Manifolds and the other on Anosov Flows on Geometric 3-Manifolds. Both topics lie at the interface of low-dimensional geometric topology (specifically, surfaces, foliations, and 3-manifolds) and low-dimensional dynamics. The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.

American Institute of Mathematics, Pasadena, California (AIM)

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying a nascent bridge between commutative algebra and symplectic geometry, with an emphasis on developing Macaulay2 software for homological computations at the interface of these two fields. Recent breakthrough work of Hanlon-Hicks-Lazarev and Favero-Huang employs symplectic techniques to build line bundle resolutions over toric varieties, resolving several conjectures in toric geometry and multigraded commutative algebra. These results have illuminated a striking new connection between commutative algebra and symplectic geometry: this workshop will bring together experts in these fields with the goal of increasing our computational power to study the interplay between them.

The Institute for Mathematical and Statistical Innovation (IMSI)

This week-long conference is in celebration of the 10-year anniversary of AATRN, the Applied Algebraic Topology Research Network. It will be the first time that AATRN meets in person, bringing together researchers from different backgrounds—mathematics, statistics, computer science, physics, biology, etc. In other words, AATRN will be “geometrically realized” at the Institute for Mathematical and Statistical Innovation in Chicago, USA!

Algebra,    Verbandstreffen für Mathematiker

Rutgers University, Newark

The focus of the workshop is the interactions of 3-manifold topology and geometry, and the study of 3-manifold groups and character and representation varieties with computational topology and theoretical computer science. We also welcome related topics! There will be several introductory lectures and longer research talks, and some short (lightning) talks. There also will be ample time for discussions and informal interactions.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to studying arithmetic dynamics of multiple maps. In classical arithmetic dynamics, we consider the iteration of a single endomorphism of a variety defined over a field of arithmetic interest — typically a number field or the function field of a curve. An exciting new direction in arithmetic dynamics that holds particular promise for striking new results is what we call "dynamics of multiple maps": dynamical behavior arising from the interaction of two or more endomorphisms on the same space. This includes iteratively applying rational functions on P1 chosen at random from a family according to some probability distribution; a correspondence from a variety X to itself; and forming words from a non-commuting family of involutions on a K3-surface.

American Institute of Mathematics, Pasadena, California (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to non-Archimedean methods in complex geometry.

On the occasion of 40+ years after the seminar paper of Gross--Zagier, we bring together experts to deliver lectures on a broad range of topics connected with the Gross-Zagier formula, its generalizations, related future directions, and other works that it has inspired.

The program will unite researchers from a number of areas: algebraic and complex geometry, arithmetic geometry, Hodge theory, and mathematical physics. It will bring theoretically and computationally oriented researchers together, expecting that computations will illuminate conjectures made by the theorists and that theory will enlarge the range of what can be computed. We intend to develop databases of certain types of K3 surfaces for the L-Functions and Modular Forms Database and promote the development of software for computations on K3 surfaces in Magma, SageMath, or other systems for public release.

Zahlentheorie, Arithmetik,    Kurse und Veranstaltungen für Studenten der Mathematik