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Algebra and Combinatorics Seminar: Mark Ebert, USC, Derived Superequivalences for Spin Symmetric Groups and Odd sl2-categorifications

SAS 2225

Since Chuang and Rouquier's pioneering work showing that categorical sl(2)-actions give rise to derived equivalences, the construction of derived equivalences has been one of the more prominent tools coming from higher representation theory. In this talk, we explain joint work with Aaron Lauda and Laurent Vera giving new super analogues of these derived equivalences stemming…

Teaching and Learning Seminar: Yan Shen, Bethany Smith, Bethanne Winzeler (DELTA), Workshop on Flipped and Hybrid course design

SAS 3282

DELTA staff will share about a course design framework and instructional tools for blended/flipped teaching and learning, as well as other teaching resources. Supported by literature in instructional design and educational psychology, the framework has been applied and improved through DELTA Grant course design projects over the past eight years, including two math courses (MA…

Department of Mathematics Fall 2022 Graduation Ceremony

SAS 2203

INVITATION TO MATHEMATICS GRADUATION CEREMONY Friday, December 16, 2022, 12:30 pm 2203 SAS Hall ~ A reception will follow the ceremony ~ Please save the date for the Department of Mathematics Fall 2022 Graduation Ceremony. Join us to celebrate the students that have earned a degree in Mathematics for Fall 2022.

Seminar: Samantha Petti, Harvard University, Probability and combinatorics in the tree of life: How stochastic processes create functional biological sequences

SAS 4201

The stochastic processes of evolution have generated DNA, RNA, and protein sequences. These sequences determine how these entities chemically interact with themselves and each other, form physical structures, and functionally behave as signals and/or machines within cells. My research involves reconstructing the history of the stochastic processes that led to the sequences we observe today…

Seminar: Farid Aliniaeifard, Generalized Chromatic Functions

SAS 4201

We define vertex-colourings for edge-coloured digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. Furthermore, we use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and quasisymmetric functions and generating functions of P-partitions. We also discuss the relations between generalized chromatic functions, Schur functions in noncommuting variables, and the well-known Stanley-Stembridge (3+1)-free conjecture.

Seminar: Gregory Handy, University of Chicago, Extending mathematical frameworks to investigate stochastic fluctuations in diverse brain cell types

SAS 4201

Stochastic fluctuations drive biological processes from particle diffusion to neuronal spike times. The goal of this talk is to use a variety of mathematical frameworks to understand such fluctuations and derive insight into the corresponding applications. We start by considering a novel stochastic process motivated by astrocytes, glial cells that ensheath neuronal synapses and can…

Seminar: Yeonjong Shin, Korea Advanced Institute of Science and Technology, Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications

SAS 4201

Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which…

Seminar: Duy Nguyen, Marist College, Continuous time optimal investment: A reinforcement learning approach

SAS 4201

In this talk, we study an exploration version of continuous time expected utility maximization problem with reinforcement learning. It is shown that the optimal feedback policy is Gaussian. We then prove a policy improvement theorem. An implementable reinforcement learning algorithm is designed. Numerical examples are provided for illustrations. Meeting ID: 957 5838 0569 Passcode: 832132

Seminar: Yairon Cid-Ruiz, Katholieke Universiteit Leuven, Belgium, Multidegrees at the crossroads of Algebra, Geometry, and Combinatorics

SAS 4201

The concept of multidegrees provides the right generalization of the degree of a projective variety to a multiprojective setting. The study of multidegrees goes back to seminal work by van der Waerden in 1929. We will slowly introduce the notion of multidegrees of a multiprojective variety. A complete characterization of the positivity of multidegrees will…

Pure Math Graduate Student Seminar: Reeshad Arian, Geometry over \mathbb{F}_1

SAS 2102

Even though the field with one element, , is a meaningless concept, shadows of it have been apparent in multiple categorical analogies. More immediately, one can generalize multiple constructions from algebraic geometry over  to general commutative monoids, which behave like rings over this elusive . In this talk we define, via this analogy, schemes over , and consider zeta…

Seminar: Di Fang, UC Berkeley, Quantum algorithms for Hamiltonian simulation with unbounded operators

SAS 4201

Recent years have witnessed tremendous progress in developing and analyzing quantum computing algorithms for quantum dynamics simulation of bounded operators (Hamiltonian simulation). However, many scientific and engineering problems require the efficient treatment of unbounded operators, which frequently arise due to the discretization of differential operators. Such applications include molecular dynamics, electronic structure theory, quantum control…

Seminar: Robert Baraldi, Sandia National Labs, An Inexact Trust Region Algorithm for Nonsmooth, Nonconvex Optimization

SAS 4201

Many problems in scientific computing require minimizing nonsmooth optimization problems. In many applications, it is common to minimize the sum of a smooth nonconvex function and a nonsmooth convex function. For example, imaging  and data science applications require minimizing a measure of data misfit plus a sparsifying L1- or total-variation regularizer.  We develop a novel…

Seminar: Michael DiPasquale, University of South Alabama, A bridge between the algebra and geometry of hyperplane arrangements

SAS 4201

A hyperplane arrangement is a union of codimension one linear spaces.  These simple objects provide fertile ground for interactions between combinatorics, algebra, algebraic geometry, topology, and group actions.  The combinatorics of an arrangement is encoded by the pattern of intersections among the hyperplanes, called its intersection lattice.  On the other hand, a key algebraic object…

Seminar: Dominykas Norgilas, University of Michigan, Model-free price bounds of derivative contracts

SAS 4201

What is the cheapest way to superhedge a path-dependent derivative security? If liquid European calls and the underlying risky stock can be used for hedging, then the lowest superhedging price corresponds to the highest expected cost of the exotic claim. Each expected cost is associated to a probabilistic model which makes the risky stock a martingale…

Seminar: Chao Chen, UT Texas, Fast, Robust, and Scalable Linear Solvers for Scientific Computing and Data Analytics

SAS 4201

The solution of large sparse linear systems is an essential building block in many science and engineering applications. It is also often the main computational bottleneck. For large problems, direct solvers (based on, e.g., LU or Cholesky factorizations) can require a significant amount of computing resources. By contrast, iterative solvers (e.g., CG and GMRES) can…

Seminar: Papri Dey, Georgia Institute of Technology, Hyperbolic Polynomials in Combinatorics and Optimization

SAS 4201

 Hyperbolic polynomials are coordinate free generalization to the notion of real rooted polynomials. A special class of hyperbolic polynomials are determinantal polynomials and they bound spectrahedra, feasible sets of semidefinite programming. I shall discuss some techniques of real algebraic geometry to deal with convex semialgebraic sets such as spectrahedra, and  demonstrate the applications of hyperbolic…

Seminar: Nadejda Drenska, Johns Hopkins University, A PDE Interpretation of Prediction with Expert Advice

SAS 4201

We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor as an investor, which converts the problem into a stock prediction problem. In this framework, an investor, who predicts the daily…

Seminar: Anna Weigandt, MIT, Combinatorial Aspects of Determinantal Varieties

SAS 4201

Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?”  These problems can be recast as questions about the structure of cohomology rings of geometric spaces such as flag varieties.  Borel’s isomorphism identifies the cohomology of the complete…