2016 - 2017
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
Some basic math things I like, where they lead and potential usages
I like the idea of a cycle representing a homology class and intersection properties of cycles and homologies. This leads to a subject called string topology. It also leads to generalizing the notion of a commutative and associative ring structure in the presence of a boundary operator.
I like locally euclidean coordinates for manifolds from rough to smooth. In various dimensions the possibilities with varying amounts of calculus have a nice pattern with a big spike in dimension four. There is a close relationship to mathematical physics models.
I like fluid motion and turbulence in dimension three. The nonlinear PDE model is currently intractable but scientists make progress by discrete approximation and simulation. I have been trying to use various math ideas to do something useful here especially using the first two sets of ideas in response to the intractability.
April 10rd, 2017
Spring Break, no seminar
April 17th, 2017
Spring Break, no seminar
April 24th, 2017
Benjamin Steinberg
The representation theory of finite monoids with applications
We give an overview of the representation theory of finite monoids and discuss some applications including finite Markov chains. No prior knowledge of these topics are assumed.
May 1st, 2017
Mahmoud Zeinalian
On the geometry and algebra of the space of all Riemann surfaces.
Making sense of the space of all geometric objects of a specific type, up to an appropriate notion of equivalence, has been a fruitful endeavor in mathematics.
For example, the fundamental theorem of algebra implies the space of all n un-ordered, not necessarily distinct, points on the 2-sphere is the n-dimensional complex projective space CP^n. Or, the space all ellipses in the plane, or any abstract 2-dimensional real vector space, that are centered at the origin, up to magnification, is a new 2-dimensional space with a natural notion of distance. This notion of distance is god-given — i.e. it doesn’t come from a choice of a metric on the plane — and makes the space of such ellipses into a model of non-Euclidean geometry.
Among more sophisticated examples are the space of all Riemann surfaces of a given genus. These spaces have interesting topology, geometry, and dynamics. In several ways, CUNY has been a center for studying these spaces.
In fact, if you consider them for all genera at once, they also become a fundamental tool in the algebraists' theory of operations with applications to the quantum theory of fields.
In this talk, I would like to explore with you some of the geometric and algebraic features of these spaces. I will discuss some actual math content and end with a description of some of the current research branches stemming from these spaces.
Fall 2016 Schedule
September 19th 2016
Louis-Pierre Arguin
The maxima of the Riemann zeta function, and branching random walks
A recent conjecture of Fyodorov, Hiary & Keating states that the maxima of the modulus of the Riemann zeta function on an interval of the critical line behave similarly to the maxima of a specific class of Gaussian fields. In this talk, we will discuss recent progress on this conjecture. We will highlight the connections between the number theory problem and the probabilistic models which include the branching random walk and the characteristic polynomial of random matrices.
September 26th, 2016
No Seminar This Week
October 3rd, 2016
No Seminar This Week
October 10th, 2016
No Seminar This Week
October 17th, 2016
Graduate Student Panel
Ivan Levcovitz, Kaethe Minden, Aradhana Kumari, Joseph Gunther
October 24th, 2016
Saeed Zakeri
Rotation Sets and Polynomial Dynamics
Rotation sets under the angle-doubling map of the circle play a key role in Douady-Hubbard's study of the quadratic family and the Mandelbrot set. This talk will outline a higher-degree analog of this idea by investigating the link between rotation sets under the multiplication by d map m(t) = d t (mod Z) of the circle and spaces of complex polynomial maps with an indifferent fixed point.
October 31st, 2016
Lucien Szpiro
From Frobenius to Lattes
I will explain my use of the Frobenius map in different subjects and also the properties of the Lattes map. As an illustration I will explain two Ph.D. obtained under my direction at the Graduate Center (A. Bhathnagar “Extending self maps to ambient projective space” and P. William “Semi-stable imply minimal resultant").
November 7th, 2016
Krysztof Klosin
Modular forms and congruences between them
Modular forms are ubiquitous in modern number theory. They are certain holomorphic functions on the complex upper half-plane which satisfy a number of symmetries. They can be studied from several different points of view, but my focus will be on their remarkable arithmetic properties. I will discuss what a modular form is, give examples and talk about what it means for two modular forms to be congruent. I will also mention some number-theoretic results which on the surface seem to have nothing to do with modular forms, but in fact their proofs have everything to do with modular forms. No background in number theory or modular forms is necessary.
November 14th, 2016
Linda Keen
Rigidity in Complex Dynamics
In this talk I will give an introduction to complex dynamics and discuss Thurston’s rigidity theorem. I’ll end by discussing some open problems arising from this theorem.
November 21st, 2016
Khalid Bou-Rabee
Detecting a group's properties through its finite quotients
Given a finitely generated group, G, what properties of G can we detect in finite group approximations of G? I will survey progress on different approaches to this broad question while touching the theories of subgroup growth, intersection growth, quantifying residual finiteness, commensurability graphs, and random walks on groups.