Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 9, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2021             April 2021              May 2021
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  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


Friday, April 9, 2021

4:00 pm in Zoom,Friday, April 9, 2021

#### The Yamabe Problem

###### Xinran Yu (UIUC)

Abstract: In a two-dimensional case, the fact that every Riemann surface has a metric with constant Gaussian curvature leads to a successful classification of Riemann surfaces. Generalizing this property to higher dimensions could be an interesting problem to consider. Thus we seek a conformal metric on a compact Riemannian manifold with constant scalar curvature. The Yamabe problem was solved in the 1980s, due to Yamabe, Trudinger, Aubin, and Schoen. Their solution to the Yamabe problem uses the techniques of calculus of variation and elliptic regularity of the Laplacian. The proof introduces a conformal invariant, so-called the Yamabe invariant, which shifts the focus from an analysis point of view to understanding a geometric invariant. The solution is separated nicely into two cases, regarding the dimension and flatness of a given Riemannian manifold. For Zoom details, please email basilio3 (at) illinois (dot) edu.

4:00 pm in Zoom,Friday, April 9, 2021

#### To Be Announced

###### Prof. Reuven Hodges   [email] (UIUC Math)

Abstract: TBA

4:30 pm in Zoom,Friday, April 9, 2021