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Graduate Student Colloquium

The Graduate Student Colloquium is geared towards introducing graduate students to different areas of mathematics.  Each week a different member of the Graduate Center Mathematics Department faculty will discuss a topic that is accessible to all graduate students.  All graduate students without an advisor are required to attend, but even those with an advisor are welcome!  Faculty members are strongly discouraged from attending.

All meetings of the Graduate Student Colloquium will be held on Mondays from 4:00-4:45 PM in the Science Center, Room 4102, unless otherwise stated.

Organizers:
Professor Alexander Gamburd: agamburd@gmail.com
Richard Gustavson: rgustavson@gradcenter.cuny.edu
Jacob Russell: jrussellmadonia@gradcenter.cuny.edu


Spring 2017 Schedule

February 27th, 2017

    No seminar

March 6th, 2017, Room 4214 (Math Lounge)

    Alice Medvedev
    What good is model theory, a branch of mathematical logic?

    Does an injective polynomial function with the same number of inputs and outputs have to be surjective? If you have n polynomials P1, P2,...,Pn in n variables x1, x2,...,xn, and the function f(x1,x2,...,xn) := (P1(x1, x2,...,xn),...,Pn(x1,x2,...,xn)) is injective, does it follow that this function f is surjective?
    
    Of course, the answer depends on where the coefficients of the polynomials and the inputs of the function come from; and on the value of n. Some instances of this question are obviously true, others are obviously false, and yet others are not so obvious. Ax used mathematical logic, together with some obvious cases, to resolve some natural non-obvious cases, such as complex numbers and n>1.

    I will present Ax's proof, identifying key logic ingredients. If time permits, I will also talk about model-theoretic versions of Galois theory and algebraic geometry - without fields, rings, or any kind of algebra.

March 13th, 2017

    Ara Basmajian
    Geometric Invariants in Hyperbolic Geometry

March 20th, 2017, Room 4214 (Math Lounge)

    Perry Susskind
    Connecticut College
    Applying for mathematics department positions at liberal arts institutions: a conversation
   
March 27th, 2017, Room 4214 (Math Lounge)

    Yunping Jiang

    An introduction to chaotic and complex dynamical systems


    I will give a brief introduction about history and recent developments in chaotic and complex dynamical systems, including period three implies chaos, Sharkovskii’s order, period doublings and the universality, Smale’s horseshoe, Julia and Fatou sets, and the Mandelbrot set. I will also mention some work we did in the past. Depending on times, I would like also to talk about the Mobius randomness and Sarnak’s conjecture in number theory which relates closely to chaotic dynamical systems.


April 3rd, 2017

    Dennis Sullivan

    TBA

April 10rd, 2017

    Spring Break, no seminar
    
April 17th, 2017

    Spring Break, no seminar

    
April 24th, 2017

    TBA

May 1st, 2017
    
    Mahmoud Zeinalian

    TBA