Thursday, February 23
1:00pm    SCGP: Math Seminar / Math of Gauge Fields: Katherine Raoux, "τ-invariants for knots in rational homology spheres"
Where:      SCGP 313When:        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."

4:00pm    Colloquium: Otis Chodosh - New results on the global geometry of scalar curvature
Where:      Math Tower P-131When:        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.
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Friday, February 24
11:00am    Am.Math.Soc. Chapter Seminar: Thomas Ng - Finite state automata and connections to group theory
Where:      Math Tower 5-127When:        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.
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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-131When:        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.
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2:30pm    Dynamical Systems Seminar: Yuri Bakhtin - Ergodic theory of the Burgers equation with random forcing
Where:      Math Tower P-131When:        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.
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4:00pm    Geometric Analysis Learning Seminar: Shaosai (Arthur) Huang - TBA
Where:      P-131 Math TowerWhen:        Fri, Feb 24    4:00pm — 6:00pm
Title:          TBA
Speaker:   Shaosai (Arthur) Huang [Stony Brook]

Abstract:    TBA
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Monday, February 27
5:30pm    First and Second Year Student Seminar: Aleksander Doan and Ruijie Yang - First and Second Year Student Seminar
Where:      Math Tower P-131When:        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.
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Tuesday, February 28
4:00pm    Geometry/Topology Seminar: Christina Sormani - Convergence of Manifolds with Nonnegative Scalar Curvature
Where:      Math Tower P-131When:        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
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Wednesday, March 1
11:30am    RTG Student Geometry Seminar: John Sheridan - Sections of semi-positive line bundles
Where:      Math Tower 5-127When:        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.
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Where:      Math Tower P-131When:        Wed, Mar 1    1:00pm — 2:00pm
Title:          TBA
Speaker:   TBA [Stony Brook]

Abstract:    TBA
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4:00pm    Algebraic geometry seminar: Dawei Chen - Extremal effective divisors on the moduli space of curves
Where:      Math Tower P-131When:        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.
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Thursday, March 2
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-131When:        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.
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Friday, March 3
1:00pm    Grad / Postdoc Professional Development Seminar: Sixth meeting
Where:      Math Tower P-131When:        Fri, Mar 3    1:00pm — 2:30pm
Title:          Sixth meeting
Speaker:   TBA [Stony Brook]

Abstract:
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2:30pm    Dynamical Systems Seminar: Kyounghee Kim - Rational Surface Automorphism: Homology actions of real mappings
Where:      Math Tower P-131When:        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.
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4:00pm    Geometric Analysis Learning Seminar: Jean-Franois Arbour - TBA
Where:      P-131 Math TowerWhen:        Fri, Mar 3    4:00pm — 6:00pm
Title:          TBA
Speaker:   Jean-Franois Arbour [Stony Brook]

Abstract:    TBA
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