[ugrads] SIAM Series of talks: My Favorite Theorem

Yue Cao ycao33 at hawk.iit.edu
Thu Nov 8 18:50:26 CST 2018

Hi, all
SIAM is holding a series of talks. The first lecture will be next Wednesday. We will offer lunch. See you there!

Series: My Favorite Theorem
This is the first talk in what we hope will become a regular series at IIT.
The talks in this series will give a light, informal introduction to the beauty of a variety of exciting theorems from around mathematics. Each talk by a faculty member (or grad student) about her/his favorite theorem will contain ideas and discussion that can be appreciated by students (undergrad and grad) as well as faculty. All members of the IIT community that appreciate (or are at least curious about) mathematics are welcome. Please get in touch with the IIT SIAM chapter if you have any questions or would like to give a talk about your favorite theorem(s).

Title: Walking through colored rooms to a fixed point
Speaker: Professor Hemanshu Kaul
Date: Wednesday, 11/14, 12:45pm-1:45pm 
Place: RE 122
I will talk about a couple of my favorite theorems, from two far apart fields of mathematics, that seem unrelated, but are in fact equivalent.
Fixed point theorems from Functional Analysis are among the most applicable theorems in mathematics. Deep theorems in other fields such as the uniqueness and existence of solutions for differential equations, and the existence of (Nash) equillibrium in n-player games, are a direct consequence of my favorite fixed point theorem by Brouwer. I will talk about how Brouwer's fixed point theorem is in fact a consequence of my favorite Combinatorial theorem, Sperner's lemma, and how a colorful walking proof of Sperner's lemma helps us find fixed points and much more.
All concepts and ideas will be (informally) defined in the talk, and all students and faculty should be able to find something of interest.

Best Regards
Yue Cao, PHD candidate
IIT SIAM Student Chapter President
Department of Applied Mathematics
Illinois of Institute of Technology

Office: John T. Rettaliata Engineering Center, Room 120
Email: ycao33 at hawk.iit.edu

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