Columbia Undergraduate Math Society

Summer 2019 <<  Fall 2019 Lectures >> Spring 2020

Wednesdays, 7:30pm; Room TBD, Mathematics
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Date Speaker Title Abstract
September 11
Raymond Cheng
Polytopes, Mixed Volumes, and Inequalities
Polytopes are higher-dimensional generalizations of polygons in the plane. Not only are they intrinsically beautiful objects, they lie at the crossroads of diverse areas of mathematics. In this talk, I will discuss a quantity associated with polytopes, called the mixed volume, the fundamental Alexandrov—Fenchel Inequality for mixed volumes, and the many connections that these quantities have with other parts of mathematics.
September 18
Stanislav Atanasov
“Number fields contain the
elements of their own transcending”
A gentle yet rapid introduction to class field theory, its conjectured generalization – the Langlands program, and the role of L-functions therein. Our starting point is a density result due to Frobenius, which implies that the Galois (hence all) extensions of a number field are uniquely determined by the set of primes that split completely. The rest of the talk traces historically the quest of understanding this set culminating in its close connection with Artin L-functions, certain meromorphic functions on the complex plane reminiscent of the Riemann zeta function.
September 25
Oleg Lazarev
 
 
October 2
 
 
 
October 9
 
 
 
October 16
 
 
 
October 23
Will Sawin
 
 
October 30
 
 
 
November 6
 
 
 
November 13
 
 
 
November 20
Alexandra Florea
 
 
November 27
 
No Meeting
 
December 4
 
 
 
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