| Date: | August 25, 2021 |
| Time: | 3:00pm |
| Location: | Blocker 624 |
| Speaker: | Nidhi Kaihnsa , Brown University |
| Title: | On Multistationarity of Phosphorylation Networks |
| Abstract: | Multistationarity in molecular systems underlies switch-like responses in
cellular decision making. Determining whether and when a system displays
multistationarity is in general a difficult problem. In joint works with
Elisenda Feliu, Timo de Wolff, and Oguzhan Yuruk we completely determine the
set of kinetic parameters that enable multistationarity in a ubiquitous motif
involved in cell signaling, namely a dual phosphorylation cycle. We also
address the same question in general for multisite phosphorylation networks. We
employ a suite of techniques from (real) algebraic geometry, which in
particular concerns the study of the signs of a multivariate polynomial over
the positive orthant and sums of nonnegative circuit polynomials.
|
|
| Date: | September 24, 2021 |
| Time: | 4:00pm |
| Location: | BLOC 302 |
| Speaker: | Zhi Jiang, U. Michigan |
| Title: | G-stable rank for tensors and its applications |
| Abstract: | G-stable rank is a new notion of rank for tensors over perfect fields, it is closely related to the stability in geometric invariant theory. We will talk about the motivation of G-stable rank and some of it's properties. We will also discuss the connection to stability. Finally, as an example, we will look at the application of G-stable rank to Cap Set problem. |
|
| Date: | October 8, 2021 |
| Time: | 4:00pm |
| Location: | BLOC 302 |
| Speaker: | F. Holweck, U. Belfort/Auburn |
| Title: | Graph states and the variety of principal minors for binary symmetric matrices. |
| Abstract: | Abstract: Graph states are special types of quantum states well studied in quantum information theory for their potential applications to quantum error correcting codes or measurement-based quantum computing. The variety of principal minors is an algebraic variety introduced by Holz and Strumfels to study the relations among principal minors of matrices. Its study also has applications to various fields such as matrix theory, probability, and computer vision. In this talk I will explain how one can build a correspondence between the graph states classification under the so-called local Clifford group and the orbits of the variety of principal minors for symmetric matrices over the 2-elements field. This is joint work with Vincenzo Galgano (Trento Univ). |
|
| Date: | October 11, 2021 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Michael Willis, Stanford University |
| Title: | Links, Braids, Infinite Twists, and More |
| Abstract: | We will consider some quantum invariants for links and braids in 3-dimensional Euclidean space, focusing on the Jones polynomial and its various "lifts" to higher categories. These invariants stand at the intersection of knot theory with more general low-dimensional topology and geometry, as well as representation theory, mathematical physics, and more. We will focus on the special role played by the limiting value of such invariants as the strands involved twist about each other infinitely often. |
|
| Date: | October 22, 2021 |
| Time: | 4:00pm |
| Location: | zoom |
| Speaker: | Daniel Grady, Texas Tech University |
| Title: | The geometric cobordism hypothesis |
| Abstract: | The cobordism hypothesis of Baez--Dolan, whose proof was sketched by Lurie, provides a beautiful classification of topological field theories: for every fully dualizable object in a symmetric monoidal (infinity,d) category, there is a unique (up to a contractible choice) topological field theory whose value at the point coincides with this object. As beautiful as this classification is, it fails to include non-topological field theories. Such theories are important not just in physics, but also in pure mathematics (for example, Yang-Mills). In this talk, I will survey recent work with Dmitri Pavlov, which proves a geometric enhancement of the cobordism hypothesis. In the special case of topological structures, our theorem reduces to the first complete proof of the topological cobordism hypothesis, after the 2009 sketch of Lurie. |
|
| Date: | October 25, 2021 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Amy Huang, Texas A&M University |
| Title: | Tensor Ranks and Matrix Multiplication Complexity |
| Abstract: | Tensors are multi-dimensional arrays. And notions of ranks and border rank abound in the literature. Tensor decompositions also have a lot of application in data analysis, physics, and other areas of science. I will try to give a colloquium-style talk surveying my current two results about tensor ranks and their application to matrix multiplication complexity. I will also briefly discuss the newest technique we used to achieve our results: border polarity. This talk assumes no background in geometry or algebra. And it is intended for a general audience. |
|
| Date: | October 29, 2021 |
| Time: | 4:00pm |
| Location: | zoom |
| Speaker: | Prasit Bhattacharya, University of Notre Dame |
| Title: | Equivariant Steenrod Operations |
| Abstract: | The classical Steenrod algebra is one of the most fundamental algebraic gadgets in stable homotopy theory. It led to the theory of characteristic classes, which is key to some of the most celebrated applications of homotopy theory to geometry. The G-equivariant Steenrod algebra is not known beyond the group of order 2. In this talk, I will recall a geometric construction of the classical Steenrod algebra and generalize it to construct G-equivariant Steenrod operations. Time permitting, I will discuss potential applications to equivariant geometry. |
|
| Date: | November 1, 2021 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | John Berman, University of Massachusetts Amherst |
| Title: | Measuring Ramification with Topological Hochschild Homology |
| Abstract: | Topological Hochschild homology (THH) has recently been popular as an approximation to algebraic K-theory, but it is also a measure of ramification in the sense of number theory. I will survey the interaction between THH and ramification / etale extensions, along with some surprising connections to classical algebraic topology. This will culminate in a new computation of THH of any ring of integers R, suggesting the philosophy: Spec(R) -> Spec(Z) is one point away from being etale. |
|
| Date: | November 4, 2021 |
| Time: | 4:00pm |
| Location: | BLOC 628 |
| Speaker: | E. Gnang, Johns Hopkins University |
| Title: | A Hypermatrix Analog of the General Linear Group |
| Abstract: | Matrices are so ubiquitous and so deeply ingrained into our mathematical lexicon that one naturally asks: “Are there higher-dimensional analogs of matrices; more importantly why bother with them at all?” In short, hypermatrices are higher-dimensional matrices. Hypermatrices are important because they broaden the scope of matrix concepts such as spectra and group actions. Hypermatrix algebras also illuminate subtle aspects of matrix algebra. In this talk we describe an instance where the transition from matrices to third order hypermatrices results in a symmetry breaking of two equivalent definitions of the matrix general linear group. We show how this transition shines a light on subtle details of invariant theory.
|
|
| Date: | November 8, 2021 |
| Time: | 3:00pm |
| Location: | zoom |
| Speaker: | V. Makam |
| Title: | Emerging applications of invariant theory to statistics |
| Abstract: | Maximum likelihood estimation is a technique in statistics that is widely used to recover the probability distribution in a statistical model that best explains the empirical data. A curious connection between stability notions in invariant theory and maximum likelihood estimation for a large class of statistical models was uncovered by Amendola, Kohn, Reichenbach, and Seigal, with recent results in complexity theory forming a bridge. In this talk, I will give an overview of these connections, present some exciting results in a few different settings and sketch out the potential future directions. I will be presenting joint work (and work in progress) combining a few projects with Gergely Berczi, Harm Derksen, Cole Franks, Eloise Hamilton, Philipp Reichenbach, Anna Seigal, and Michael Walter. |
|
| Date: | November 15, 2021 |
| Time: | 3:00pm |
| Location: | zoom |
| Speaker: | Tim Seynnaeve, U. Bern |
| Title: | Enumerative geometry for algebraic statistics and semidefinite programming |
| Abstract: | In statistics, the maximum likelihood degree of a statistical
model measures the algebraic complexity of maximum likelihood estimation. In
convex optimization, the algebraic degree of semidefinite programming
measures the algebraic complexity of solving the KKT equations. We
discovered that both of these numbers have an interpretation in terms of
classical problems in enumerative geometry. To phrase it in a more modern
language: they are intersection numbers on the variety of complete quadrics.
As an application, we prove a conjecture by Sturmfels and Uhler stating that
the maximum likelihood degree behaves polynomially. This illustrates both
how methods from algebraic geometry can be used to prove conjectures arising
in applications, but also how drawing inspiration from applications gives
rise to new geometric questions. This talk is based on joint projects with
Rodica Dinu, Laurent Manivel, Mateusz Michalek, Leonid Monin, and Martin
Vodicka. |
|
| Date: | November 19, 2021 |
| Time: | 4:00pm |
| Location: | zoom |
| Speaker: | Gleb Smirnov, ETH, Zurich |
| Title: | Symplectic mapping class groups of K3 surfaces |
| Abstract: | I will briefly introduce symplectic mapping class groups and explain how to use Seiberg-Witten theory to get information about them. In particular, I will prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated, thus extending a recent result of Sheridan and Smith. Time permitting, we will also discuss the elliptic version of the story, where K3 is replaced with a blow-up of the complex torus.
|
|
Menu