Mon, Oct 12
Algebra Seminar
Dr. Anand P. Sawant, Tata Institute of Fundamental Research, Mumbai, India and SLMath, Berkeley, CA.
Weil restriction, cellular structures and Milnor-Witt K-theory
4:00 PM, 250 Math Building
The category of strictly \(\mathbb{A}^1\)-invariant sheaves is central to the development of \(\mathbb{A}^1\)-algebraic topology over a field. It is a nontrivial fact that this is an abelian, symmetric monoidal category. In this talk based on joint work with Fabien Morel, I will outline a fundamental computation in this category, namely that of the tensor product of the Milnor-Witt K-theory sheaf with the so-called free strictly \(\mathbb{A}^1\)-invariant sheaf on a point, defined over a finite separable field extension of the base field. The computation is made possible by cellular \(\mathbb{A}^1\)-homology introduced in our earlier joint work.
Mon, Oct 19
Algebra Seminar
Mark Shimozono (Virginia Tech)
Realizations of equivariant homology of affine Grassmannians in symmetric functions
4:00 PM, 250 Math Building
It has been known since the 1970s that the cohomology ring of the Grassmannian is a quotient of the ring of symmetric functions with the Schubert basis indexed by certain Schur functions, allowing the computation of intersection numbers for Schubert classes via combinatorics. Analogously we will describe symmetric function realizations of the equivariant homology and cohomology of affine Grassmannians of reductive algebraic groups of classical type.
Mon, Oct 19
Applied Mathematics Seminar
Baofeng Teng, The University of Texas Rio Grande Valley
Soliton solutions on an elliptic background
4:00 PM, 122 Mathematics Building
In this talk, we will present a framework to construct various soliton solutions for integrable PDEs on an elliptic background. First, we will establish elliptic analogues of AKP, BKP, CKP and DKP hierarchies, as well as their tau functions expressed by Weierstrass elliptic functions. Then by the Kadomtsev–Petviashvili (KP) reduction method, breather and rogue wave solutions on an elliptic background can be derived systematically. This is a joint work with my Ph.D student: Changyan Shi.
Tue, Oct 20
What is...? Seminar
Johanna Mangahas
TBA
4:00 PM, 250 Mathematics Building
TBA
Thu, Oct 22
Colloquium
Sahana Balasubramanya (Lafayette College)
Extending acylindricity to higher rank- an overview
4:00 PM, Mathematics Building
I will present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-) acylindrically on finite products of hyperbolic spaces. This work (joint with T. Fernos) is inspired by the classical theory of S-arithmetic lattices and that of acylindrically hyperbolic groups. I will start with the motivation for studying these groups in this talk, and cover some results we have proved that highlight this duality.