Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 25, 2022.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
    February 2022            March 2022             April 2022     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5          1  2  3  4  5                   1  2
  6  7  8  9 10 11 12    6  7  8  9 10 11 12    3  4  5  6  7  8  9
 13 14 15 16 17 18 19   13 14 15 16 17 18 19   10 11 12 13 14 15 16
 20 21 22 23 24 25 26   20 21 22 23 24 25 26   17 18 19 20 21 22 23
 27 28                  27 28 29 30 31         24 25 26 27 28 29 30

Friday, March 25, 2022

1:00 pm in 147 Altgeld Hall,Friday, March 25, 2022
Graduate Analysis Seminar

Index theorems and boundary conditions

Gayana Jayasinghe (UIUC)

Abstract: The study of the Fredholm Index of operators is of great interest in analysis. The 60's saw the development of the theory of the index of elliptic operators as a topological invariant on compact manifolds, a vast generalization of the Gauss Bonnet theorem. Now there are generalizations of all sorts of spaces including spaces with boundary, singularities and in non commutative geometry. I will begin by introducing Index theory, motivating the key ideas with the example of the Gauss Bonnet theorem, on manifolds with boundary. The index in this example has a topological contribution as well as a contribution coming from the asymmetry of the boundary, which can be described in terms of geodesic curvature. I will then describe how for general operators, this asymmetry can be expressed using boundary conditions for the operator, and in the case of spectral boundary conditions, one deals with the spectral asymmetry. I won't assume any prior knowledge on Index theory, and it should be accessible for analysts

Submitted by ryanm12
3:00 pm in 341 Altgeld Hall,Friday, March 25, 2022
Graduate Student Homotopy Theory Seminar

An introduction to 2-categories

Yigal Kamel (UIUC Math)

Abstract: This talk will be a survey of some of the basic notions and facts about 2-categories. After introducing 2-categories and various types of functors between them, we will consider constructions that map 2-categories to more familiar objects. On one hand, viewing a 2-category as a “poor” higher category, we can “reduce” it to an ordinary category, via a homotopy construction. On the other hand, viewing a 2-category as a “rich” ordinary category, we can “uplift” it to a simplicial set, via the duskin nerve. I will talk about these and related ideas, indicate some quirks of the theory, and provide examples along the way.

Submitted by doronlg2
4:00 pm in 347 Altgeld Hall,Friday, March 25, 2022
Graduate Geometry and Topology Seminar

Modular Forms in Geometry and Physics

Saaber Pourmotabbed

Abstract: Modular forms appear as generating functions of curve counts and BPS states, partition functions of conformal field theories, in moonshine phenomena, sections of line bundles, spectrums of cohomology theories, elliptic genera of K3 surfaces, and many other interesting cases. In this talk we will look at some examples of where modular forms occur in physics and geometry, why they occur, and their interactions between these different fields.

Submitted by wsmilde2