Wednesday January 24, 2018 1:00 PM  2:00 PM Math Tower P131
 Xujia Chen, Stony Brook University
Belyi's theorem and dessin d'enfantsEvery compact Riemann surface can be realized as the normalization of an algebraic curve in P^2. Belyi's theorem states that a compact Riemann surface S can be written as the normalization of an algebraic curve defined by a polynomial F, all of whose coefficients are algebraic numbers, if and only if there exists a branched covering from S to P^1 with at most three branch values. Such a Riemann surface with such a branched covering is called a Belyi pair. Belyi pairs are in onetoone correspondence to a certain kind of graphs, dessin d'enfants (``children's drawing''), which are defined purely combinatorially. I will begin from the definition and basic properties of Riemann surfaces. Belyi's theorem will not be proved, but I will explain the general idea and give part of the proof if time permits.

Wednesday January 31, 2018 1:00 PM  2:00 PM Math Tower P131
 Saman Habibi Esfahani, Stony Brook University
Combinatorial Knot Floer HomologyKnot Floer homology is an invariant for knots and links in 3manifolds. We will see a combinatorial description of this invariant and some of its applications in low dimensional topology, including Milnor's conjecture about Torus knots.

Wednesday February 07, 2018 1:00 PM  2:00 PM Math Tower P131
 Aleksandar Milivojevic, Stony Brook University
Computations in Cartande Rham homotopy theoryThe sizable differential graded algebra of forms on a smooth manifold admits a tractable model which contains more homotopy information than the real cohomology algebra. We will determine this model for several manifolds, compute some higher homotopy groups modulo torsion, and discuss how to model fiber bundles.

Wednesday February 14, 2018 1:00 PM  2:00 PM Math Tower P131
 Nathan Chen, Stony Brook University
Elliptic Curves and the Monster groupThere are several perspectives that one can take with regards to elliptic curves. We will first classify them up to biholomorphism using the $j$invariant, and then explore the relationship between the $j$invariant and the Monster group. You donut want to miss this talk!

Wednesday February 21, 2018 1:00 PM  2:00 PM Math Tower P131
 Prithviraj Chowdhury, Stony Brook University
TBATBA

Wednesday February 28, 2018 1:00 PM  2:00 PM Math Tower P131
 JeanFrançois Arbour, Stony Brook University
TBATBA

Wednesday March 07, 2018 1:00 PM  2:00 PM Math Tower P131
 Hang Yuan, Stony Brook University
TBATBA

