1:00pm **SCGP:** Math Seminar / Math of Gauge Fields: Katherine Raoux, "τ-invariants for knots in rational homology spheres"

**Where:** SCGP 313**When:** Thu, Feb 23 1:00pm — 2:00pm

**Speaker:** Katherine Raoux

**Title:** τ-invariants for knots in rational homology spheres

**Abstract:** Using the knot filtration on the Heegaard Floer chain complex, Ozsváth and Szabó defined an invariant of knots in the three sphere called τ(K), which they also showed is a lower bound for the 4-ball genus. Generalizing their construction, I will show that for a (not necessarily null-homologous) knot, K, in a rational homology sphere, Y, we may obtain a collection of τ-invariants, one for each spin-c structure. We also show that these invariants can be used to obtain a lower bound on the genus of a surface with boundary K properly embedded in a negative definite 4-manifold with boundary Y

2:30pm **YITP:** YITP Seminar, Hiren Patel (UMass, Amherst)

**When:** Thu, Feb 23 2:30pm — 3:30pm

"Package-X: A Mathematica package for the analytic calculation of one loop integrals"

"Package-X is a Mathematica package for the fully analytic calculation of one-loop Feynman integrals. In this talk I will highlight the capabilities of Package-X using a selection of familiar examples, and summarize some of the novel algorithms driving the program. I will close the talk with possible directions for future development."

"Package-X: A Mathematica package for the analytic calculation of one loop integrals"

"Package-X is a Mathematica package for the fully analytic calculation of one-loop Feynman integrals. In this talk I will highlight the capabilities of Package-X using a selection of familiar examples, and summarize some of the novel algorithms driving the program. I will close the talk with possible directions for future development."

4:00pm Colloquium: Otis Chodosh - New results on the global geometry of scalar curvature

**Where:** Math Tower P-131**When:** Thu, Feb 23 4:00pm — 5:00pm

**Title:** New results on the global geometry of scalar curvature

**Speaker:** Otis Chodosh [Princeton University/IAS]

**Abstract:** I'll survey some recent results concerning the global behavior of minimal/constant mean curvature surfaces in three manifolds with non-negative scalar curvature. Co-authors for these works include M. Eichmair, V. Moraru, Y. Shi, and H. Yu.

View Details

View Details

11:00am Am.Math.Soc. Chapter Seminar: Thomas Ng - Finite state automata and connections to group theory

**Where:** Math Tower 5-127**When:** Fri, Feb 24 11:00am — 12:00pm

**Title:** Finite state automata and connections to group theory

**Speaker:** Thomas Ng [Temple University]

**Abstract:** Representing group elements in an efficient manner is impossible due to pathological examples such as those with unsolvable word problem. A finite state automaton(FSA) is a combinatorial tool from computation theory than can encode word theoretic properties of certain "well-behaved" groups for example the fundamental group of a surfaces or a hyperbolic 3-manifolds and braid groups. This structure can be use to algorithmically study algebraic, geometric, and probabilistic properties of these groups. We will start by introducing FSAs and how Thurston's notion of an automatic group provides fast solutions to the word problem and quadratic bounds on the isoperimetric function of the Cayley graph. We will also discuss how spectral properties of the automaton can be used to effectively study the growth of a group as well as random/generic group elements. One theme is that computationally simple groups have nice properties and there are many of them.

View Details

View Details

12:00pm Grad / Postdoc Professional Development Seminar: Robert Lazarsfeld - What does the AMS do, and why should we all belong to it?

**Where:** Math Tower P-131**When:** Fri, Feb 24 12:00pm — 1:20pm

**Title:** What does the AMS do, and why should we all belong to it?

**Speaker:** Robert Lazarsfeld [Stony Brook]

**Abstract:** This week, Rob Lazarsfeld will give an overview of some of things that the American Mathematical Society does to support mathematics in the United States (in particular various AMS programs aimed at younger mathematicians). As always, pizza will be served.

View Details

View Details

2:30pm Dynamical Systems Seminar: Yuri Bakhtin - Ergodic theory of the Burgers equation with random forcing

**Where:** Math Tower P-131**When:** Fri, Feb 24 2:30pm — 3:30pm

**Title:** Ergodic theory of the Burgers equation with random forcing

**Speaker:** Yuri Bakhtin [Courant Institute of Mathematical Sciences]

**Abstract:** The Burgers equation is a basic nonlinear evolution PDE of Hamilton--Jacobi type related to fluid dynamics and growth models. I will talk about the ergodic theory of randomly forced Burgers equation in noncompact setting. The basic objects are one-sided infinite minimizers of random action (in the inviscid case) and polymer measures on one-sided infinite trajectories (in the positive viscosity case). This is joint work with Eric Cator, Kostya Khanin, and Liying Li.

View Details

View Details

4:00pm Geometric Analysis Learning Seminar: Shaosai (Arthur) Huang - TBA

**Where:** P-131 Math Tower**When:** Fri, Feb 24 4:00pm — 6:00pm

**Title:** TBA

**Speaker:** Shaosai (Arthur) Huang [Stony Brook]

**Abstract:** TBA

View Details

View Details

5:30pm First and Second Year Student Seminar: Aleksander Doan and Ruijie Yang - First and Second Year Student Seminar

**Where:** Math Tower P-131**When:** Mon, Feb 27 5:30pm — 6:30pm

**Title:** First and Second Year Student Seminar

**Speaker:** Aleksander Doan and Ruijie Yang [Stony Brook]

**Abstract:** As young mathematicians, Aleksander and Ruijie will share some of their experience and tips of doing research.

View Details

View Details

4:00pm Geometry/Topology Seminar: Christina Sormani - Convergence of Manifolds with Nonnegative Scalar Curvature

**Where:** Math Tower P-131**When:** Tue, Feb 28 4:00pm — 5:30pm

**Title:** Convergence of Manifolds with Nonnegative Scalar Curvature

**Speaker:** Christina Sormani [Lehman College and CUNY Graduate Center]

**Abstract:** I will survey conjectures, examples and results about sequences of three dimensional manifolds with nonnegative scalar curvature. Some of the conjectures are stated in recent work of Gromov, in recent work of mine, and in joint work of mine with Lee. I will present partial results towards some of these conjectures completed with Huang-Lee, with Stavrov, and with LeFloch, and techniques related to the intrinsic flat convergence of manifolds appearing in joint work with Lakzian, with Portegies, and alone. Finally I will present examples constructed with Basilio. See arxiv1606.08949

View Details

View Details

11:30am RTG Student Geometry Seminar: John Sheridan - Sections of semi-positive line bundles

**Where:** Math Tower 5-127**When:** Wed, Mar 1 11:30am — 12:30pm

**Title:** Sections of semi-positive line bundles

**Speaker:** John Sheridan [Stony Brook]

**Abstract:** We will discuss how to construct sections of line bundles on tori using Fourier series. This will allow us to compute the dimension of the space of holomorphic sections of the line bundle in terms of the corresponding data described in the Appel-Humbert Theorem. Finally, we will address the issue of determining ampleness.

View Details

View Details

1:00pm Graduate Student Seminar: TBA

**Where:** Math Tower P-131**When:** Wed, Mar 1 1:00pm — 2:00pm

**Title:** TBA

**Speaker:** TBA [Stony Brook]

**Abstract:** TBA

View Details

View Details

4:00pm Algebraic geometry seminar: Dawei Chen - Extremal effective divisors on the moduli space of curves

**Where:** Math Tower P-131**When:** Wed, Mar 1 4:00pm — 5:30pm

**Title:** Extremal effective divisors on the moduli space of curves

**Speaker:** Dawei Chen [Boston College]

**Abstract:** The cone of effective divisors governs central properties of a variety. Knowing the shape of the effective cone amounts to understanding extremal effective divisors that span the boundary rays of the cone. In this talk I will give an introduction to this topic, with a focus on the case when the underlying variety is the moduli space of curves. If time permits I will also talk about extremal effective cycles of higher codimension.

View Details

View Details

2:30pm **YITP:** YITP seminar, Ciaran Williams

**When:** Thu, Mar 2 2:30pm — 3:30pm

4:00pm Colloquium: Arseniy Akopyan - Waists of balls in different spaces

**Where:** Math Tower P-131**When:** Thu, Mar 2 4:00pm — 5:00pm

**Title:** Waists of balls in different spaces

**Speaker:** Arseniy Akopyan [MCCME]

**Abstract:** Gromov and Memarian (2003-2011) have established the waist inequality asserting that for any continuous map f from the sphere $S^n \to R^{n-k}$ there exists a fiber $f^{-1}(y)$ such that every its t-neighborhood has measure at least the measure of the t-neighborhood of an equatorial subsphere $S^k$ of $S^n$.

Going to the limit we may say that the (n-k)-volume of the fiber $f^{-1}(y)$ is at least that of the standard sphere $S^k$. We extend this limit statement to the exact bounds for balls in spaces of constant curvature, tori, parallelepipeds, projective spaces and other metric spaces.

By the volume of preimages for a non-regular map f we mean its lower Minkowski content, some new properties of which will be also presented in the talk.

View Details

Going to the limit we may say that the (n-k)-volume of the fiber $f^{-1}(y)$ is at least that of the standard sphere $S^k$. We extend this limit statement to the exact bounds for balls in spaces of constant curvature, tori, parallelepipeds, projective spaces and other metric spaces.

By the volume of preimages for a non-regular map f we mean its lower Minkowski content, some new properties of which will be also presented in the talk.

View Details

1:00pm Grad / Postdoc Professional Development Seminar: Sixth meeting

**Where:** Math Tower P-131**When:** Fri, Mar 3 1:00pm — 2:30pm

**Title:** Sixth meeting

**Speaker:** TBA [Stony Brook]

**Abstract:**

View Details

View Details

2:30pm Dynamical Systems Seminar: Kyounghee Kim - Rational Surface Automorphism: Homology actions of real mappings

**Where:** Math Tower P-131**When:** Fri, Mar 3 2:30pm — 3:30pm

**Title:** Rational Surface Automorphism: Homology actions of real mappings

**Speaker:** Kyounghee Kim [Florida State University]

**Abstract:** Let f:X -> X be a quadratic rational surface automorphism fixing a cuspidal cubic. Let X_R be the closure of RP^2 inside X. When the multiplier at the invariant cuspidal cubic is real, f induces an automorphism f_R of X_R. In this talk, we discuss an algorithm for calculating the homology action of f_R, and we make several observations on the homology action. This is joint work with J. Diller.

View Details

View Details

4:00pm Geometric Analysis Learning Seminar: Jean-Franois Arbour - TBA

**Where:** P-131 Math Tower**When:** Fri, Mar 3 4:00pm — 6:00pm

**Title:** TBA

**Speaker:** Jean-Franois Arbour [Stony Brook]

**Abstract:** TBA

View Details

View Details