## Programs & Events

##### Research Community in Algebraic Combinatorics

Feb 10 - 11, 2022

The Women in Algebraic Combinatorics Research Community will bring together researchers at all stages of their careers in algebraic combinatorics, from both research and teaching-focused institutions, to work in groups of 4-6, each directed by a leading mathematician. The goals of this program are: to advance the frontiers of cutting-edge algebraic combinatorics, including through explicit computations and experimentation, and to strengthen the community of women working in algebraic combinatorics.

Successful applicants will be assigned to a group based on their research interests. The groups will work on open problems in algebraic combinatorics and closely related areas, including representation theory, special functions, and discrete geometry. Several of the proposed projects will extensively involve experimentation and computation, which will increase the likelihood that concrete progress is made over the course of the initial workshop and following 6 months, and provide useful... (more)

##### Organizing Committee

- Susanna Fishel
- Pamela E. Harris
- Rosa Orellana
- Stephanie van Willigenburg

##### Holistic Design of Time-Dependent PDE Discretizations

Jan 10 - 14, 2022

The workshop aims to spur a holistic approach to the design of time-dependent PDE discretizations, particularly in terms of developing time integration techniques that are intertwined with spatial discretization techniques, focusing on: generalized ImEx methods, asymptotic-preserving and structure-preserving methods, methods that exploit low-rank dynamics, analysis of order reduction, parallel in time methods, and performant, maintainable, extensible software implementations.

Recent decades have seen increasing use of first-principles-based simulations via time-dependent partial differential equations (PDE), with applications in astrophysics, climate science, weather prediction, marine science, geosciences, life science research, defense, and more. Growing computational capabilities have augmented the importance of sophisticated high-order and adaptive methods over â€œnaive'â€ low-order methods. However, there are fundamental challenges to achieving truly high order and full... (more)

##### Organizing Committee

- David Ketcheson
- David Keyes
- Michael Minion
- Jingmei Qiu
- Benjamin Seibold
- Carol Woodward

##### VIRTUAL ONLY: Prediction and Variability of Air-Sea Interactions: the South Asian Monsoon

Aug 23 - 27, 2021

A challenge for mathematical modeling, from toy dynamical system models to full weather and climate models, is applying data assimilation and dynamical systems techniques to models that exhibit chaos and stochastic variability in the presence of coupled slow and fast modes of variability. Recent collaborations between universities and government agencies in India and the United States have resulted in detailed observations of oceanic and atmospheric processes in the Bay of Bengal, the Arabian Sea, and the Indian Ocean, collectively observing manyÂ coupled modes of variability. One key target identified by these groups was the improvement of forecasts of variability of the summer monsoon, which significantly affects agriculture and water management practices throughout South Asia.Â The Monsoon Intraseasonal Oscillation is a northward propagating mode of precipitation variability and is one of the most conspicuous examples of coupled atmosphere-ocean processes during the summer... (more)

##### Organizing Committee

- Baylor Fox-Kemper
- Jennifer MacKinnon
- Hyodae Seo
- Emily Shroyer
- Aneesh Subramanian
- Amit Tandon

##### VIRTUAL ONLY: Spectra LGBTQ+ in Mathematics Conference

Aug 18 - 20, 2021

Spectra, the Association for LGBTQ+ Mathematicians, was conceived in the last ten years with its first official event in 2015 -- a panel discussion at the JMM in San Antonio. Since then, Spectra has organized events at various conferences to bring together people of the LGBTQ+ community.

Spectra is organizing this conference to provide opportunities for LGBTQ+ mathematicians both to celebrate achievements and to spark conversations of challenges in our community. This will be a space for attendees to share their research across all areas of mathematics (theoretical, applied, and math education) and to interact and create support networks within and across their research communities.

Spectra is proud to organize its first official conference and create an intentional space for LGBTQ+ mathematicians. This will be an event where LGBTQ+ mathematicians at all career stages can interact and network with their peers. Further, it will facilitate discussions for creating better environments... (more)

##### Organizing Committee

- Rustum Choksi
- David Crombecque
- Alexander Hoover
- Brian Katz
- Freda Li
- Claire Plunkett
- Konstantina Trivisa
- Alexander Wiedemann

##### VIRTUAL ONLY: D-modules, Group Actions, and Frobenius: Computing on Singularities

Aug 9 - 13, 2021

The adoption of D-module techniques has transformed the interface between commutative algebra and algebraic geometry over the last two decades. The discovery of interactions and parallels with the Frobenius morphism has been an impetus for many new results, including new invariants attached to singularities but also D- and F-module based algorithms for computing quantities that used to be unattainable.

Our goal for this workshop is to discuss computational aspects and new challenges in singularity theory, focusing on special varieties that arise from group actions, canonical maps, or universal constructions. By bringing together geometers, algebraists, and invariant theorists, we will address problems from multiple perspectives. These will include comparisons of composition chains for D- and F-modules, the impact of group actions on singularity invariants, and the structure of differential operators on singularities in varying characteristics.

##### Organizing Committee

- Christine Berkesch
- Linquan Ma
- Claudia Miller
- Claudiu Raicu
- Uli Walther

##### VIRTUAL ONLY: Research Community in Algebraic Combinatorics

Aug 5 - 6, 2021

The Women in Algebraic Combinatorics Research Community will bring together researchers at all stages of their careers in algebraic combinatorics, from both research and teaching-focused institutions, to work in groups of 4-6, each directed by a leading mathematician. The goals of this program are: to advance the frontiers of cutting-edge algebraic combinatorics, including through explicit computations and experimentation, and to strengthen the community of women working in algebraic combinatorics.

Successful applicants will be assigned to a group based on their research interests. The groups will work on open problems in algebraic combinatorics and closely related areas, including representation theory, special functions, and discrete geometry. Several of the proposed projects will extensively involve experimentation and computation, which will increase the likelihood that concrete progress is made over the course of the initial workshop and following 6 months, and provide useful... (more)

##### Organizing Committee

- Susanna Fishel
- Pamela E. Harris
- Rosa Orellana
- Stephanie van Willigenburg

##### VIRTUAL ONLY: Applications of Rough Paths: Computational Signatures and Data Science

Jul 6 - 9, 2021

Rough path theory emerged as a branch of stochastic analysis to give an improved approach to dealing with the interactions of complex random systems. In that context, it continues to resolve important questions, but its broader theoretical footprint has been substantial. Most notable is its contribution to Hairerâ€™s Fields-Medal-winning work on regularity structures. At the core of rough path theory is the so-called signature transform which, while being simple to define, has rich mathematical properties bringing in aspects of analysis, geometry, and algebra. Hambly and Lyons (Annals of Math, 2010) built upon earlier work of Chen, showing how the signature represents the path uniquely up to generalized reparameterizations. This turns out to have practical implications allowing one to summarise the space of functions on unparameterized paths and data streams in a very economical way.

Over the past five years, a significant strand of applied work has been undertaken to exploit the... (more)

##### Organizing Committee

- Thomas Cass
- Terry Lyons
- Hao Ni
- Harald Oberhauser
- Mihaela van der Schaar

##### VIRTUAL ONLY: Computational Aspects of Discrete Subgroups of Lie Groups

Jun 14 - 18, 2021

This workshop is at the interface of algebra, geometry, and computer science. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representations of groups and their geometric properties. The setting of linear Lie groups is amenable to calculation and modeling transformations, thus providing a bridge between algebra and its applications.

The main goal of the proposed workshop is to synergize and synthesize the independent strands in the area of computational aspects of discrete subgroups of Lie groups. We aim to facilitate solutions of theoretical problems by means of recent advances in computational algebra and additionally stimulate development of computational algebra oriented to other mathematical disciplines and applications.

##### Organizing Committee

- Alla Detinko
- Michael Kapovich
- Alex Kontorovich
- Peter Sarnak
- Richard Schwartz

##### VIRTUAL ONLY: Advances and Challenges in Hyperbolic Conservation Laws

May 17 - 21, 2021

In the field of hyperbolic conservation laws, theory, computation, and applications are deeply connected, with each one providing to the other two technical support as well as insights. Major progress has been achieved, over the past 40 years, on the theory and computation of solutions in one space dimension. By contrast, the multi-space dimensional case is still covered by mist, which is now gradually lifting, revealing new vistas. For instance, in two space dimensions, significant progress has been achieved in the study of transonic gas flow, of central importance to aerodynamics. Parallel progress has been reported on the numerical side, with the design of high-order accurate discontinuous Galerkin and finite volume computational schemes, even for multidimensional systems. Finally, we are witnessing an explosion in the applications, not only on the traditional turf of fluid dynamics but also in new directions, in materials science, biology, traffic theory, etc.

Nevertheless, the... (more)

##### Organizing Committee

- Alberto Bressan
- Gui-Qiang Chen
- Constantine Dafermos
- Fengyan Li
- Chi-Wang Shu
- Eitan Tadmor
- Konstantina Trivisa
- Dehua Wang

##### VIRTUAL ONLY: USTARS

Apr 29 - 30, 2021

The primary mission of the Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is to showcase the excellent research conducted by underrepresented students studying topology and algebra. Dedicated to furthering the success of underrepresented students, USTARS seeks to broaden participation in the mathematical sciences by cultivating research and mentoring networks. USTARS is open to all people interested in the topological and algebraic fields.

A note from the organizing committee:

Applicants, for those wanting to give a talk at the conference there is an application deadline of February 26 at 11:59 pm for speakers in order to make a timely decision. We have funding from the NSA for some per diem for both days of the conference, which will also be decided from applicants who apply by the deadline. If you do receive funding, you are required to attend the entire conference.

##### Organizing Committee

- Robyn Brooks
- Ty Frazier
- Paige Helms
- Ryan Moruzzi Jr
- Anisah Nuâ€™Man
- Christopher O'Neill
- Javier Ronquillo Rivera
- Sherilyn Tamagawa

##### VIRTUAL ONLY: Symmetry, Randomness, and Computations in Real Algebraic Geometry

Aug 24 - 28, 2020

Real algebraic (and semi-algebraic) geometry studies subsets of R^n defined by a finite number of polynomial equalities and inequalities. Such sets occur ubiquitously in practice both inside and outside of mathematics. While being easy to define, semi-algebraic sets can be complicated topologically, which restricts the application of many algorithms. In recent years, there has been progress in proving much stronger results â€“ both quantitative and algorithmic -- when the problem under consideration involves the invariance under some group action.

In this workshop, we plan to focus on two situations where this phenomenon happens.

The first one is the statistical study of the topology of random real algebraic varieties as well as semi-algebraic sets, where the polynomials defining these objects are picked from a distribution invariant under the action of a certain group (usually the orthogonal group) acting on the space of variables. The behavior of the set of zeros (or more... (more)

##### Organizing Committee

- Saugata Basu
- Antonio Lerario
- Annie Raymond
- Cordian Riener

##### VIRTUAL ONLY: Free Resolutions and Representation Theory

Aug 3 - 7, 2020

The structure of free resolutions plays an important role in analyzing singularities of varieties of low codimension. Codimension 2 Cohen-Macaulay varieties (resp. codimension 3 Gorenstein varieties) come from rank conditions on an n x (n+1) matrix (resp. a skew-symmetric (2n+1) x (2n+1) matrix).

This workshop seeks to push such results to Cohen-Macaulay varieties of codimension 3 and Gorenstein varieties of codimension 4.

This problem turns out to be related to the classification of semi-simple Lie algebras. These new methods allow one to create a â€˜mapâ€™ of free resolutions of a given format. The calculations that arise are very demanding and require new computational methods involving both commutative algebra and representation theory.

The organizers have shared two sets of notes for attendees to review before the workshop. These are downloadable here:

##### Organizing Committee

- Lars Christensen
- Claudia Miller
- Steven Sam
- Jerzy Weyman