Wednesday February 20, 2019 4:00 PM  5:30 PM Math Tower P131
 Algebraic geometry seminar Junliang Shen, MIT
Perverse filtrations, GopakumarVafa invariants, and hyperkähler geometryFor a hyperkähler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse tstructure. We will discuss the role played by this filtration in the study of the topology and geometry of hyperkähler varieties, as well as the connection to curve counting invariants of CalabiYau 3folds. In particular, we will discuss some recent progress on the P=W conjecture for Hitchin systems, and its compact analog for Lagrangian fibrations. Based on joint work with Qizheng Yin and Zili Zhang.

Wednesday February 20, 2019 2:30 PM  3:30 PM Math Tower P131
 Mini Course / Dynamics Learning Seminar ByungGeun Oh, Hanyang University
Combinatorial GaussBonnet Theorem and its applicationsIn this talk we will start with the concept of combinatorial curvature on planar graphs. After brief explanation for some progress related to combinatorial curvature, the main topic of this talk will come in, the "combinatorial GaussBonnet theorem". Definitely it is the combinatorial counterpart to GaussBonnet theorem in differential geometry. We will especially focus on the GaussBonnet formula involving boundary (left) turns, since we found at least two reasonable applications of it.
The first application is related to the HeSchramm conjecture [1] about types of disk circle packing, which was later proved by Repp [2]. During the talk a statement stronger than the HeSchramm conjecture(i.e., Repp's theorem) will be presented, and one will see that the stronger version can be proved in a simpler way.
The next application is about isoperimetric constants on planar graphs. Suppose a given planar graph has faces and vertices whose degrees are at least $p$ and $q$, respectively, where $p$ and $q$ are natural numbers such that $1/p + 1/q < 1/2$.Then it is natural to guess that the isoperimetric constant of this graph is at least that of the $(p,q)$regular graph, the $q$regular planar graph all of whose faces have the same degree $p$. This `guess' was in fact conjectured by Lawrencenko, Plummer, and Zha [3], for which we could give an affirmative answer using the combinatorial GaussBonnet theorem. A sketch of the proof will be given if time allows.
[1] Z. He and O. Schramm, Hyperbolic and parabolic packings, Discrete Comput. Geom. 14 (1995), no. 2, 123149.
[2] A. Repp, Bounded valence excess and the parabolicity of tilings, Discrete Comput. Geom. 26 (2001), no. 3, 321351.
[3] S. Lawrencenko, M. Plummer, and X. Zha, Isoperimetric constants of infinite plane graphs, Discrete Comput. Geom. 28 (2002), no. 3, 313330.

Wednesday February 20, 2019 1:00 PM  2:00 PM Math Tower P131
 Graduate Student Seminar Taras Kolomatski, Stony Brook University
An Infinite Quantum Ramsey TheoremNik Weaver (2015) showed an intriguing noncommutative version of the classical Ramsey's theorem on graphs: Let $\mathcal{V}$ be a subspace of $M_n(\mathbb{C})$ which contains the identity matrix and is stable under the formation of Hermitian conjugates. If $n$ is sufficiently large, then there is a rank $k$ orthogonal projection such that $\dim (P\mathcal{V}P)$ is $1$ or $k^2$. These are the minimal and maximal possibilities for this dimension, and in these cases such a projection is called a quantum $k$anticlique or quantum $k$clique, respectively.
Weaver further showed that both the classical and quantum Ramsey's theorems are special cases of a general Ramsey theorem on \textit{quantum graphs}, which are modelled on such matrix spaces with the additional algebraic structure of being a bimodule of some matrix $*$algebra. Investigation of such objects was initially motivated by quantum information theory, in which quantum graphs provided an analogue of the confusability graph in classical communication over a noisy channel. Weaver's work follows a long list of results successfully generalising classical results to this context, such as the definition of quantum Shannon capacity by Duan, Severini and Winter (2013).
In this talk, I will look at salient examples that demonstrate the difference between the classical and quantum contexts, sketch Weaver's results, and describe the process by which we successfully adapted Weaver's work demonstrate a quantum analogue of the classical infinite Ramsey's theorem in Kennedy, Kolomatski, Spivak (2017). Working in this infinite dimensional setting required functional analysis, and invited plenty of delightful nuance in topological considerations.

Wednesday February 20, 2019 4:00 PM Math Tower 5127
 Analysis Student Seminar Jacob Mazor, Stony Brook University
First considerations in regularity theoryWe finish our introduction to currents by looking at the case of codimension 1 currents: this is special as integral currents of codimension 1 were in fact introduced before the foundational paper by Federer and Fleming, by De Giorgi and Caccioppoli as sets of finite perimeter.
We then move on to discuss some first considerations in regularity theory: after an overview of the known regularity results for codimension 1 and for higher codimension, we will start developing some preliminaries, such as monotonicty formulas and its consequences.

Thursday February 21, 2019 4:00 PM  5:00 PM Math Tower P131
 Colloquium Ernie Croot, Georgia Tech
Long Progressions in SumsetsAn old question in additive number theory is determining the length of the longest progression in a sumset A+B = {a + b : a in A, b in B}, given that A and B are "large" subsets of {1,2,...,n}. I will survey some of the results on this problem, including a discussion of the methods, and also will discuss some open questions and conjectures.

Friday February 22, 2019 10:00 AM  11:00 AM Math Tower 5127
 RTG Student Geometry Seminar Lisa Marquand, Stony Brook University
The Dolbeault GroupoidIn this talk, we define the Dolbeault groupoid of rank one Higgs bundles over a compact Riemann surface. We will focus on explaining how hermitian metrics relate unitary connections to holomorphic line bundles.

Friday February 22, 2019 2:30 PM  3:30 PM Math Tower P131
 Dynamical Systems Seminar Kasra Rafi, University of Toronto
Counting of the number of simple closed curves on a surface, revisitedTBA

Tuesday February 26, 2019 1:00 PM  2:30 PM P131
 Grad / Postdoc Professional Development Seminar Stony Brook Faculty, Stony Brook University
Applying for NSF grantsWith Aliakbar Daemi, Bob Hough, Mark Mclean, and Christian Schnell. Each of us is going to talk about their experience with writing a grant proposal, applying to the NSF, getting feedback from the NSF, etc. We'll share some of the documents, and of course answer questions. We'll also be happy to give specific advice to those of you who are thinking about applying for a grant this fall.

Wednesday February 27, 2019 4:00 PM  5:30 PM Math Tower P131
 Algebraic geometry seminar Benjamin Bakker, University of Georgia
Hodge theory and ominimalityThe cohomology groups of complex algebraic varieties come equipped with a powerful invariant called a Hodge structure. Going back to foundational work of Griffiths, Hodge theory has found many important applications to algebraic and arithmetic geometry, but its intrinsically analytic nature often leads to complications. Recent joint work with Y. Brunebarbe, B. Klingler, and J. Tsimerman has shown that in fact many Hodgetheoretic constructions can be carried out in an intermediate geometric category, and ominimality provides the crucial tameness hypothesis to make this precise. In this talk I will describe how this perspective can be used to easily recover an important theorem of CattaniDeligneKaplan on the algebraicity of Hodge loci and to prove a conjecture of Griffiths on the quasiprojectivity of the images of period maps.

Thursday February 28, 2019 4:00 PM  5:00 PM Math Tower P131
 Colloquium Benjamin Bakker, University of Georgia
ominimal GAGAA complex algebraic variety can be naturally considered as a complex analytic space. Working with the analytic space often has many advantages, as for instance there are many more complex analytic functions than algebraic ones. For this perspective to be useful in algebraic geometry, it is necessary to also go backwardsthat is, to characterize when analytic constructions starting with algebraic varieties return algebraic varieties. One powerful answer to this question is provided by Serre's celebrated GAGA theorem. It generalizes an earlier result of Chow asserting that closed complex analytic subspaces of a compact algebraic variety are in fact algebraic. Both of these theorems easily fail for noncompact algebraic varieties.
In this talk I will explain joint work with Y. Brunebarbe and J. Tsimerman which shows that Serre's GAGA theorem extends to the noncompact case if one restricts to analytic structures that are "tame" in a sense made precise by the modeltheoretic notion of ominimality. We will also explain why this result has important applications to Hodge theory.

Friday March 01, 2019 2:30 PM  3:30 PM Math Tower P131
 Dynamical Systems Seminar Zoran Sunic, Hofstra University
Schreier spectra of some iterated monodromy groupsWe discuss calculation of spectra of several iterated monodromy groups, such as the Hanoi Towers group $H$ and one of its subgroups, the “tangled odometers group“ $T$.
The Hanoi Towers group is the iterated monodromy group of the $3$dimensional, postcritically finite, rational map $z→ z^2 – 16/(27z)$ and it models the wellknown Hanoi Towers Problem. The subgroup $T$ is the iterated monodromy group of the postcritically finite, cubic polynomial $z→ z^3/2 + 3z/2$ whose two critical points are fixed.
The groups act on the ternary rooted tree and on its boundary. The spectrum of the Schreier graphs of these actions were, in both cases, shown to consist of a countable set of isolated points and a Cantor set to which the isolated points accumulate via backward iterations of a quadratic polynomial. In both cases, the calculation is facilitated by first introducing a higher dimensional rational map, which is then shown to be semiconjugate to a onedimensional map.
Time permitting, we will also discuss the case of iterated monodromy groups of arbitrary conservative polynomials.

Tuesday March 05, 2019 1:00 PM  2:30 PM P131
 Grad / Postdoc Professional Development Seminar Graduate students, Stony Brook University
Recital practice IPractice meeting for the graduate student recitals on March 26/27. Please attend and give some feedback to the speakers!

Thursday March 07, 2019 2:30 PM P131
 Analysis Seminar Guy David, Ball State University
Lipschitz differentiability, embeddings, and rigidity for group actionsWe discuss a class of metric spaces that, despite being nonEuclidean, support a firstorder calculus for Lipschitz functions developed by Cheeger. After introducing these spaces, we will survey some of their embedding properties and explain a theorem of the speaker and Kyle Kinneberg concerning embeddings in Carnot groups. Then we will explain an application of this last result to a problem on group actions in hyperbolic geometry.

Thursday March 07, 2019 4:00 PM  5:00 PM Math Tower P131
 Colloquium Stephen Miller, Rutgers University
Sphere packing, Fourier interpolation, and the Universal Optimality TheoremI will discuss recent work on the optimal arrangement of points in euclidean space. In addition to the solution to the sphere packing problem in dimensions 8 and 24 from 2016, the "Universal Optimality" conjecture has now been proved in these dimensions as well. This shows that E8 and the Leech lattice minimize energy for any completely monotonic function of distancesquared, a fact which was previously not known for any configuration of points in any dimension > 1. Beyond giving a new proof of these sphere packing results, Universal Optimality also gives information about longrange interactions. Another application is to find the global minimum of the logdeterminant of the laplacian among flat tori in those dimensions. The techniques involve arranging both a function and its Fourier transform to vanish at certain points, which leads to a new interpolation formula that recovers a radial Schwartz function from the values of it, its Fourier transform, and their derivatives, at special arithmetic points. Finally, fitting with the theme of the “Automorphic Structure” workshop, the interpolation formula reduces to an identity involving modular forms. (joint with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska)

Tuesday March 12, 2019 1:00 PM  2:30 PM P131
 Grad / Postdoc Professional Development Seminar Graduate students, Stony Brook University
Recital practice IIPractice meeting for the graduate student recitals on March 26/27. Please attend and give some feedback to the speakers!

Tuesday March 12, 2019 4:00 PM  5:00 PM Math Tower P131
 Geometry/Topology Seminar Fedor Manin, Ohio State University
Rational homotopy and topological isoperimetrySoon after Sullivan introduced his model of rational homotopy theory in the 1970's, Gromov noted that the theory had some metric consequences for maps between compact manifolds or simplicial complexes. I will present a systematic view of this relationship which gives a powerful tool for, among other things, resolving the following type of question, asked by Gromov twenty years later:
Given two $L$Lipschitz maps $f, g: X → Y$, where $X$ and $Y$ are nice compact metric spaces, what is the optimal Lipschitz constant of a homotopy between them?
I will also try to explain why this question is fundamental to quantitative topology.

Wednesday March 13, 2019 4:00 PM  5:30 PM Math Tower P131
 Algebraic geometry seminar Dan Abramovich, Brown University
Resolving singularities in familiesSemistable reduction is often the first step in constructing
compactified moduli spaces, and can be used to discover their
properties. I will describe workinprogress with Michael Temkin and
Jaroslaw Wlodarczyk in which we prove functorial semistable reduction
for families of varieties in characteristic 0, refining work with Karu
from 2000. Techniques developed for moduli spaces enter in unexpected
ways.

Thursday March 14, 2019 2:30 PM P131
 Analysis Seminar Lutz Warnke, Georgia Tech
TBATBA

Tuesday March 26, 2019 4:00 PM  5:00 PM S240
 Special Lectures Graduate students, Stony Brook University
Graduate student recitals 1

Wednesday March 27, 2019 4:00 PM  5:30 PM S240
 Special Lectures Graduate students, Stony Brook University
Graduate student recitals 2

Wednesday March 27, 2019 2:30 PM  3:30 PM Math Tower P131
 Mini Course / Dynamics Learning Seminar Jonathan Fraser, University of St Andrews
Dimensions of Kleinian limit setsThe dimension theory of geometrically finite Kleinian groups and their limit sets has a rich and interesting history, with the first calculation of Hausdorff dimension going back to seminal work of Patterson and Sullivan from the 1970s and 80s. There are many different (but related) notions of dimension but, nevertheless, many of the most popular coincide in this setting. In particular, the Hausdorff, boxcounting, and packing dimensions of a Kleinian limit set are all given by the Poincare exponent of the group. I will discuss recent work concerning the Assouad dimension, which is not necessarily given by the Poincare exponent in the presence of parabolic points.

Thursday March 28, 2019 4:00 PM  5:00 PM SCGP Auditorium
 Colloquium Simon Donaldson, SCGP
TBA

Thursday March 28, 2019 2:30 PM P131
 Analysis Seminar Sean Li, University of Connecticut
TBA

Tuesday April 02, 2019 4:00 PM  5:30 PM Math Tower P131
 Geometry/Topology Seminar Simons Lectures, Stony Brook University
no Geometry/Topology seminar

Thursday April 04, 2019 2:30 PM P131
 Analysis Seminar Michael Damron, Georgia Tech
TBATBA

Thursday April 11, 2019 2:30 PM P131
 Analysis Seminar LiCheng Tsai, Columbia University
TBATBA

Thursday April 25, 2019 1:00 PM  2:15 PM Math Tower 5127
 Seminar in Topology and Symplectic Geometry Rukmini Dey, ICTSTIFR, Bangalore
The Quillen Determinant Bundle and Geometric Quantization of Various Moduli SpacesTBA

Thursday April 25, 2019 4:00 PM  5:00 PM Math Tower P131
 Colloquium John Morgan, SCGP
TBA

Thursday May 02, 2019 2:30 PM P131
 Analysis Seminar Hoi Nguyen, Ohio State University
TBATBA

