1:00pm Graduate Student Seminar: Taras Kolomatski - An Infinite Quantum Ramsey Theorem

**Where:** Math Tower P-131**When:** Wed, Feb 20 1:00pm — 2:00pm

**Title:** An Infinite Quantum Ramsey Theorem

**Speaker:** Taras Kolomatski [Stony Brook University]

**Abstract:** Nik Weaver (2015) showed an intriguing non-commutative 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.

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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.

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2:00pm **SCGP:** Physics Seminar: Ibou Bah

**Where:** SCGP 313**When:** Wed, Feb 20 2:00pm — 3:00pm

**Title:** Anomaly Inflow for M5-branes wrapping a Riemann Surface

**Abstract:** In this talk we discuss the ’t Hooft anomalies for theories on the world volume of M5-branes wrapping a punctured Riemann Surface. We show how to compute them from the geometric setup in M-theory by using anomaly inflow. In particular, we explain how the boundary data for the M5-branes at a puncture is encoded onto the M-theory geometry. This allows for a derivation of the contributions to the anomalies from the punctures. We also discuss the relations between the inflow setup and holography.

2:30pm Mini Course / Dynamics Learning Seminar: Byung-Geun Oh - Combinatorial Gauss-Bonnet Theorem and its applications

**Where:** Math Tower P-131**When:** Wed, Feb 20 2:30pm — 3:30pm

**Title:** Combinatorial Gauss-Bonnet Theorem and its applications

**Speaker:** Byung-Geun Oh [Hanyang University]

**Abstract:** In 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 Gauss-Bonnet theorem". Definitely it is the combinatorial counterpart to Gauss-Bonnet theorem in differential geometry. We will especially focus on the Gauss-Bonnet formula involving boundary (left) turns, since we found at least two reasonable applications of it.

The first application is related to the He-Schramm conjecture [1] about types of disk circle packing, which was later proved by Repp [2]. During the talk a statement stronger than the He-Schramm 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 Gauss-Bonnet 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, 123-149.

[2] A. Repp, Bounded valence excess and the parabolicity of tilings, Discrete Comput. Geom. 26 (2001), no. 3, 321-351.

[3] S. Lawrencenko, M. Plummer, and X. Zha, Isoperimetric constants of infinite plane graphs, Discrete Comput. Geom. 28 (2002), no. 3, 313-330.

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The first application is related to the He-Schramm conjecture [1] about types of disk circle packing, which was later proved by Repp [2]. During the talk a statement stronger than the He-Schramm 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 Gauss-Bonnet 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, 123-149.

[2] A. Repp, Bounded valence excess and the parabolicity of tilings, Discrete Comput. Geom. 26 (2001), no. 3, 321-351.

[3] S. Lawrencenko, M. Plummer, and X. Zha, Isoperimetric constants of infinite plane graphs, Discrete Comput. Geom. 28 (2002), no. 3, 313-330.

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4:00pm Algebraic geometry seminar: Junliang Shen - Perverse filtrations, Gopakumar-Vafa invariants, and hyper-khler geometry

**Where:** Math Tower P-131**When:** Wed, Feb 20 4:00pm — 5:30pm

**Title:** Perverse filtrations, Gopakumar-Vafa invariants, and hyper-khler geometry

**Speaker:** Junliang Shen [MIT]

**Abstract:** For a hyper-khler variety equipped with a Lagrangian fibration, an increasing filtration is defined on its rational cohomology using the perverse t-structure. We will discuss the role played by this filtration in the study of the topology and geometry of hyper-khler varieties, as well as the connection to curve counting invariants of Calabi-Yau 3-folds. 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.

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4:00pm Analysis Student Seminar: Jacob Mazor - First considerations in regularity theory

**Where:** Math Tower 5-127**When:** Wed, Feb 20 4:00pm — 5:00pm

**Title:** First considerations in regularity theory

**Speaker:** Jacob Mazor [Stony Brook University]

**Abstract:** We 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.

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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.

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1:00pm **SCGP:** Hitchin Systems Program Seminar: Fabio Apruzzi

**Where:** SCGP 313**When:** Thu, Feb 21 1:00pm — 2:30pm

**Title:** Non-flat elliptically fibered Calabi-Yau threefolds in F/M-theory and phases of five-dimensional superconformal field theories.

**Abstract:** The main subject of this talk are Calabi-Yau threefolds with certain type of canonical singularities. These can be viewed as genus one fibration with a section (elliptic) over a complex two-dimensional base. The elliptic fiber degenerates at codimension-one and two in the base, where codimension-two singularities are not of Kodaira type. I will then describe certain (crepant) resolutions of these singular Calabi-Yau threefolds, where the dimension of the fiber jumps at one point in the base, but the base remains unchanged. These geometric objects, once interpreted in F/M-theory, are relevant to study phases of five-dimensional superconformal field theories (5D SCFTs), enhanced global symmetries, and their relation to circle compactifications of 6D SCFTs. The geometric understanding of the enhanced global symmetries of the 5D SCFTs is also motivated by the study and classification of parabolic and wild/irregular Hitchin systems.

2:30pm **YITP:** Pheno Seminar: Oren Slone (Princeton)

**When:** Thu, Feb 21 2:30pm — 3:30pm

4:00pm Colloquium: Ernie Croot - Long Progressions in Sumsets

**Where:** Math Tower P-131**When:** Thu, Feb 21 4:00pm — 5:00pm

**Title:** Long Progressions in Sumsets

**Speaker:** Ernie Croot [Georgia Tech]

**Abstract:** An 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.

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10:00am RTG Student Geometry Seminar: Lisa Marquand - The Dolbeault Groupoid

**Where:** Math Tower 5-127**When:** Fri, Feb 22 10:00am — 11:00am

**Title:** The Dolbeault Groupoid

**Speaker:** Lisa Marquand [Stony Brook University]

**Abstract:** In 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.

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2:30pm Dynamical Systems Seminar: Kasra Rafi - Counting of the number of simple closed curves on a surface, revisited

**Where:** Math Tower P-131**When:** Fri, Feb 22 2:30pm — 3:30pm

**Title:** Counting of the number of simple closed curves on a surface, revisited

**Speaker:** Kasra Rafi [University of Toronto]

**Abstract:** TBA

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4:00pm Geometric Analysis Learning Seminar: Demetre Kazaras - Bray's proof of the Penrose Conjecture

**Where:** P-131 Math Tower**When:** Fri, Feb 22 4:00pm — 6:00pm

**Title:** Bray's proof of the Penrose Conjecture

**Speaker:** Demetre Kazaras [Stony Brook University]

**Abstract:**

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2:30pm **SCGP:** Weekly Physics Meeting: Nikita Nekrasov

**Where:** 313**When:** Mon, Feb 25 2:30pm — 3:30pm

**Title:** Codimension two defects in supersymmetric gauge theories, Painleve VI and classical/quantum correspondence

1:00pm Grad / Postdoc Professional Development Seminar: Stony Brook Faculty - Applying for NSF grants

**Where:** P-131**When:** Tue, Feb 26 1:00pm — 2:30pm

**Title:** Applying for NSF grants

**Speaker:** Stony Brook Faculty [Stony Brook University]

**Abstract:** With 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.

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4:15pm **SCGP:** Physics Colloquium: Ruth Angus

**Where:** Harriman 137**When:** Tue, Feb 26 4:15pm — 5:15pm

Coffee and Tea at 3:45

Full Schedule: http://www.physics.sunysb.edu/Physics/colloquium/2018/

Coffee and Tea at 3:45

Full Schedule: http://www.physics.sunysb.edu/Physics/colloquium/2018/

2:00pm **SCGP:** Physics Seminar: Shu Heng Shao

**Where:** SCGP 313**When:** Wed, Feb 27 2:00pm — 3:00pm

**Title:**

**Abstract:**

4:00pm Algebraic geometry seminar: Benjamin Bakker - Hodge theory and o-minimality

**Where:** Math Tower P-131**When:** Wed, Feb 27 4:00pm — 5:30pm

**Title:** Hodge theory and o-minimality

**Speaker:** Benjamin Bakker [University of Georgia]

**Abstract:**

The 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 Hodge-theoretic constructions can be carried out in an intermediate geometric category, and o-minimality 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 Cattani--Deligne--Kaplan on the algebraicity of Hodge loci and to prove a conjecture of Griffiths on the quasiprojectivity of the images of period maps.

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The 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 Hodge-theoretic constructions can be carried out in an intermediate geometric category, and o-minimality 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 Cattani--Deligne--Kaplan on the algebraicity of Hodge loci and to prove a conjecture of Griffiths on the quasiprojectivity of the images of period maps.

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