Meetings/Workshops on Algebra in the United States (USA)

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Courses and Events for Math Students and Early Career Researchers,    Geometry and Topology

Mathematical Sciences Research Institute (MRSI)

This workshop is built around four minicourses that will introduce the participants to a range of recent techniques in various areas of holomorphic dynamics, given by specialists in these topics. The event is complemented by a series of talks by leaders in the field, aimed at a large audience and presenting current research directions in the area.

Complex Networks,    Complex Systems, Chaos and Self-Organisation

Georgia College & State University, Department of Mathematics

The Southern Regional Algebra Conference is an annual weekend conference that has been in existence since 1988. It serves an important role as part of the algebra research community in the Gulf Coast Region. Graduate students are strongly encouraged to participate. There is no registration fee. Presentations will be 25 minutes in length. The deadline to submit abstracts for SRAC 2022 is March 1, 2022. The Conference will be held on the campus of Georgia College & State University in Milledgeville, GA, March 18-20, 2022. The program will start on Friday, March 18, 2022 at 1 PM and end on Sunday, March 20, 2022 at 12:30 PM.

Phone: [4784450974];     Email: guy.biyogmam@gcsu.edu

ICERM

Incarnations of braid groups, or generalizations thereof, naturally arise in a range of active research areas in symplectic and algebraic geometry. This is a rich and diverse ecosystem, and the workshop will aim to bring together speakers from all corners of it. A unifying theme is monodromy: one the one hand, generalized braid groups arise in symplectic and algebraic geometry as fundamental groups of moduli spaces, loosely construed -- for instance, of complements of discriminant loci of singularities or of hyperplane arrangements, or moduli spaces of deformations of complex or symplectic structures. On the other hand, monodromy ideas motivate representations of generalized braid groups as various flavors of geometric automorphisms -- for instance, as (framed) mapping class group elements, symplectic Dehn twists, spherical twists in derived categories, or flop functors for 3-folds. These perspectives lead in turn to a wide array of further geometric applications, from classifications of Stein fillings to the study of spaces of Bridgeland stability conditions.

From a community perspective, one aim of the workshop is to bring together mathematicians from adjacent research communities with a shared interest in braids as they arise in symplectic or algebraic geometry. We hope the conference will accelerate the cross-pollination of ideas, and help foster collaborations, at what is a very exciting time for the field. Much of this research also lies at an interface with other aspects of the thematic semester -- for instance, braids in representation theory (e.g. in connection with cluster algebras or Bridgeland stability conditions), or in low-dimensional topology (e.g. in connection with monodromies of open books) -- and many of the talks should be of interest to a broader set of semester participants.

Phone: [401 863 5030];     Email: info@icerm.brown.edu

Mathematical Sciences Research Institute (MRSI)

This workshop will explore connections between the regularity theory of minimal surfaces and of mean curvature flow. Recent breakthroughs have improved our understanding of singularity formation in both settings but the current research trends are becoming increasingly disparate. Experts from both areas will present their research and there will be ample free time to establish connections between the topics.

The aim of this workshop is to bring together researchers whose work contributes to the study of random structures that exhibit some form of conformal self-similarity. Notable examples include the Schramm-Loewner evolution SLE, the Brownian map and random trees, Liouville Quantum Gravity, and Conformal Field Theory. A particular focus will be the discussion of analytic tools needed to address the challenges arising from the often rough underlying sets and spaces.

Mathematical Sciences Research Institute (MRSI)

The aim of this workshop is to bring together researchers whose work contributes to the study of random structures that exhibit some form of conformal self-similarity. Notable examples include the Schramm-Loewner evolution SLE, the Brownian map and random trees, Liouville Quantum Gravity, and Conformal Field Theory. A particular focus will be the discussion of analytic tools needed to address the challenges arising from the often rough underlying sets and spaces.

This workshop will focus on complex dynamics in one and several variables. We will bring toghether experts in rational dynamics, transcendental dynamics, and dynamics in several complex variables in order to get new perspective and foster discussions in a warm and stimulating atmosphere. A special focus will be put on the interactions between one dimensional and higher dimensional complex dynamics, and on connections with adjacent areas of mathematics.

Cornell University

We are excited to announce that the 7th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals will be held June 4, 2022 - June 8, 2022. After two consecutive cancellations due to Covid, we are currently planning the 2022 Fractals Conference. As normalcy returns to our lives, we look forward to hosting an in-person conference once again, collaborating with colleagues around the world, and sharing each others knowledge.

Ergodic Schrödinger operators have been studied heavily since the 1970s, as they include many examples of physical interest, such as disordered media, electrons in an external magnetic field, and quasicrystals. These operators enjoy many subtle connections to other areas of mathematics, such as dynamical systems, topology, and group theory. The study of quantum graphs stems from the modeling of thin waveguides arranged into a topological network. Such models appeared already in the 1930s but have experienced a surge in popularity in recent years. Recent works have exploited connections between these two fields; these developments have scratched the surface of a much larger opportunity for collaboration. Thus, the aim of this workshop is to bring these two communities together for two purposes: to disseminate recent results, and to foster collaboration and communication between these communities.

CCAAGS-22 aims to bring together researchers working in the creative mixture of combinatorial and computational ideas in applied algebraic geometry. Part of this event will celebrate Bernd Sturmfels and his contributions to the field.

Graph Theory and Combinatorics,    Geometry and Topology

Mathematical Sciences Research Institute (MRSI)

Courses and Events for Math Students and Early Career Researchers,    Calculus, Differential Equations and Integration

The Symmetries in Graphs, Maps, and Polytopes Workshop has been providing researchers interested in symmetries of discrete objects and structures to meet, share results, discuss open problems, and start new collaborations every four years since its inaugural meeting in 1998 in Flagstaff, Arizona. SIGMAP2022 will be held at the University of Alaska Fairbanks, and will provide an intimate setting for learning about recent developments in the study of symmetry of discrete geometric objects such as graphs, maps, polytopes, and maniplexes, discussing open problems in the area, and forming collaborations to tackle them.

University of Colorado Boulder

The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. This will be a problem set focused summer school surrounding four mini-courses.

1) Fixed point theory and Nielsen theory 2) Categorical Approach to Duality 3) Spectra 4) Trace Methods

Mathematical Sciences Research Institute (MRSI)

The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.

Courses and Events for Math Students and Early Career Researchers,    Geometry and Topology

MRSI – Mathematical Sciences Research Institute, Berkeley

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.

Mathematical Sciences Research Institute (MRSI)

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

The last several years have seen rapid development of a new language for conformal field theory(CFT), including insights from the conformal bootstrap program. This conference will bring to bear the modern arsenal of conformal field theory on the foundations of holography and quantum gravity. A theme of the conference will be the extent to which consistency conditions on quantum gravity are inherited from those of CFT, and whether they naturally lead to string/M-theory. By bringing together scientists on both sides of holographic duality, we hope to explore these issues in a broad way.Topics to be covered include large N bootstrap and the structure of holographic CFTs dual to general relativity; CFT sum rules and gravitational effective field theory; aspects of supersymmetry in holography; low-dimensional holography, modularity and quantum chaos; black holes from strongly-coupled finite temperature physics; symmetry constraints on gravitational path integrals and AdS vacua; S-matrices, their relation to CFT correlators, and holography away from AdS.

Astronomy, Astrophysics and Cosmology,    Mathematical Physics

Mathematical Sciences Research Institute (MRSI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.

Mathematical Sciences Research Institute (MRSI)

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.

Algebraic Cycles, L-Values, and Euler Systems