Columbia Undergraduate Math Society

Fall 2015« Spring 2016 Lectures »Summer 2016

Wednesdays, 7:30pm; Room 507, Mathematics
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ums [at] math.columbia.edu

Date Speaker Title Abstract
Jan 27 Carl Lian Lines in 3-space Given four (sufficiently general) lines in 3-space, how many lines intersect all four? To answer this question, we will introduce some fundamental notions in algebraic geometry and intersection theory. We will attempt to keep the discussion as elementary as possible.
Feb 3 Rob Castellano

Boundaries of manifolds and classical
mechanics

One of the first questions that one can ask is "what geometric objects are boundaries of other geometric objects?" This question turns out to be very important and, depending on the context, also interesting. This talk will go over some basic topology and introduce the field of symplectic geometry.
Feb 10 Anand Deopurkar Fermat's last theorem for polynomials Fermat's last theorem says that X+ Y= Zn has no non-trivial solutions for integers X, Y, Z, if n > 2. We will prove Fermat's last theorem where "integers" is replaced by "polynomials" (in one variable). We will see many different proofs, some elementary and some more sophisticated, using ideas from algebra, topology, and algebraic geometry.
Feb 17 Vivek Pal TBD (Number theory)  
Feb 24 James Cornish TBD (Knot theory)  
March 2 Alex Zhang TBD (Symplectic topology)  
March 9 Feiqi Jiang An application of modular forms  
March 16 Spring break    
March 23 Daniel Halpern-Leistner The representation theory of sl2  
March 30 Daniel Litt TBD  
April 6 Pak-Hin Lee TBD  
April 13 Ina Petkova TBD  
April 20 Simon Brendle TBD  
April 27 Karsten Gimre TBD  
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