Sep 20

Myhill Lecture #3
Laura DeMarco
4:00PM, Fri Sep 20 2019

Sep 23

Piotr Hajac, IMPAN; (Adam Sikora)

4:00PM, Mon Sep 23 2019, Math 250

Noncommutative Chern-Weil theory and homotopy invariance of Hochschild and
cyclic complexes

Goodwillie’s theorem states that the periodic cyclic homology is invariant under nilpotent extensions. We discuss a special type of nilpotent extensions of unital algebras called row extensions.
They appear in abundance, and are always H-unital but generically non-unital and noncommutative. For these special nilpotent extensions, we prove a stronger result: the homotopy invariance
of Hochschild and cyclic complexes. A very specific type of a row extension appears naturally in
the construction of the Chern-Galois character. If P is an algebra with a principal coaction, and
B is its subalgebra of coaction invariants, then the Chern-Galois character factors through the row
extension of B by the nilpotent ideal consisting of the invariant universal differential one-forms
on P. When P is a principal comodule algebra, one can identify this ideal with the kernel of the
multiplication map restricted to the algebra of the associated Ehresmann-Schauenburg quantum
groupoid. For any principal coaction, all this leads to the Chern-Weil homomorphism defined on
the space of cotraces.
Based on joint work with Tomasz Maszczyk.

Sep 25

Mariusz Tobolski (Hanfeng Li) Mathematics Polish Academy of Sciences

Wednesday, September 25, 2019

A classical result from topology states that if X is a principal G-bundle over a paracompact space M, then there exists a map from M to the classifying space BG, and all isomorphic principal G-bundles are classified by the homotopy class of such a map. The aim of this talk is to find an analog of this result in the realm of noncommutative topology, where instead of topological spaces and groups, we consider C*-algebras and quantum groups respectively. First, we introduce the notion of a locally trivial noncommutative principal bundle in the setting of compact quantum group actions on C*-algebras. Then, for a compact quantum group G, we define the C*-algebra of functions on the noncommutative classifying space C(BG) and prove that it classifies all locally trivial noncommutative principal G-bundles.

Sep 26

Colloquium: Piotr M. Hajac

4:00PM, Thu Sep 26 2019

Noncommutative Chern-Weil theory and homotopy invariance of Hochschild and
cyclic complexes


Goodwillie’s theorem states that the periodic cyclic homology is invariant under nilpotent extensions. We discuss a special type of nilpotent extensions of unital algebras called row extensions.
They appear in abundance, and are always H-unital but generically non-unital and noncommutative. For these special nilpotent extensions, we prove a stronger result: the homotopy invariance
of Hochschild and cyclic complexes. A very specific type of a row extension appears naturally in
the construction of the Chern-Galois character. If P is an algebra with a principal coaction, and
B is its subalgebra of coaction invariants, then the Chern-Galois character factors through the row
extension of B by the nilpotent ideal consisting of the invariant universal differential one-forms
on P. When P is a principal comodule algebra, one can identify this ideal with the kernel of the
multiplication map restricted to the algebra of the associated Ehresmann-Schauenburg quantum
groupoid. For any principal coaction, all this leads to the Chern-Weil homomorphism defined on
the space of cotraces.
Based on joint work with Tomasz Maszczyk.

Sep 27

G&T Seminar
Subhankar Dey (UB)
4:00PM, Fri Sep 27 2019, 122 Mathematics Building

Sep 30

Aparna Upadhyay, UB
4:00PM, Mon Sep 30 2019, Math 250

Oct 1

Kristofer Reyes (UB Department of Materials Design and Innovation)
4:00PM, Tue Oct 1 2019, Math 250

Oct 2

Yi Wang (Hanfeng Li)

4:00PM, Wed Oct 2 2019, Math 250

In this talk, I will introduce a sharp inequality relating a parameterized set of weighted Bergman norms and the Hardy norm on the unit disk.  The original form of this inequality can be traced back to to 1921, when Carleman provided a complex analytic proof of the famous isoperimetric theorem.  In recent years, the inequality has regained attention because of its application in number theory.  By taking a close examination of the derivatives of the norms with respect to the parameter, we obtain some sufficient conditions for the inequliaty to hold.  This is joint work with Hui Dan and Kunyu Guo.

Oct 8

Applied math seminar: Erdem Sariyuce
4:00PM, Tue Oct 8 2019

Oct 9

Xiaocheng Li, University of Wisconsin
4:00PM, Wed Oct 9 2019

Oct 17

Colloquium: Barry Fox
A Quant’s Journey Toward Diversification
4:00PM, Thu Oct 17 2019

Portfolio diversification is a useful technique that has the potential to improve risk-adjusted returns for an investment portfolio. In this presentation we take a detailed look at diversification through theoretical considerations as well as empirical results. We analyze the degree of potential benefit of diversification as well as its limitations and trade-offs. This provides a glimpse into quantitative research conducted by Graham Capital’s systematic investment team.

Oct 22

Applied math seminar: Mark Hoefer
4:00PM, Tue Oct 22 2019

Oct 23

Han Li, Wesleyan University ( Hanfeng Li)
4:00PM, Wed Oct 23 2019

Nov 19

Anita T. Layton (University of Waterloo)

4:00PM, Tue Nov 19 2019

Math 250