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 ScheduleFebruary 27th, 2017 No seminarMarch 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 P_{1}, P_{2},...,P in _{n}n variables x, and the function _{1}, x_{2},...,x_{n}f(x) := (_{1},x_{2},...,x_{n}P(_{1}x),...,_{1}, x_{2},...,x_{n}P(_{n}x_{1},x)) is injective, does it follow that this function _{2},...,x_{n}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 GeometryMarch 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 JiangAn 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, 2017Dennis Sullivan TBAApril 10rd, 2017 Spring Break, no seminar April 17th, 2017 Spring Break, no seminarApril 24th, 2017 TBAMay 1st, 2017 Mahmoud Zeinalian TBA |

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