Department of

# Mathematics

Seminar Calendar
for events the day of Monday, December 2, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, December 2, 2019

3:00 pm in 441 Altgeld Hall,Monday, December 2, 2019

#### The Gross-Hopkins duality

###### Ningchuan Zhang (UIUC Math)

Abstract: In this talk, we introduce the Gross-Hopkins duality in chromatic homotopy theory, which relates the the Spanier-Whitehead duality and the Brown-Comenetz duality in the $K(n)$-local category. We will mainly focus on the underlying algebraic geometry of the duality phenomena and work out some explicit examples at height 1.

3:00 pm in 243 Altgeld Hall,Monday, December 2, 2019

#### A path approach to holonomy for singular foliations

###### Joel Villatoro (KU Leuven)

Abstract: This talk concerns a joint project with Alfonso Garmendia. The holonomy groupoid is a fundamental invariant of foliation theory. An important advance in the understanding of singular foliations when Androulidakis and Skandalis showed how to construct a topological groupoid that generalized the usual holonomy groupoid of a classical foliation. A drawback to their approach was that the construction of the groupoid itself was radically different to the traditional construction of the holonomy groupoid. In this talk, I will explain another way to construct the same object which is a more straightforward generalization of the classical construction.

5:00 pm in 241 Altgeld Hall,Monday, December 2, 2019

#### Dixmier Trace

###### Haojian Li (UIUC)

Abstract: 1. Recap some basic facts of pseudo differential operators. 2. Pseudo differential calculus. (adjoint and multiplication) 3. Regularity. 4. Modulated operator. (if time permitting)