1:00pm Topology and Symplectic Geometry / Math of Gauge Fields seminar: Sara Venkatesh - Quantitative symplectic cohomologyQuantitative symplectic cohomology

**Where:** MAT 5-127**When:** Thu, Apr 26 1:00pm — 2:00pm

**Title:** Quantitative symplectic cohomology

Quantitative symplectic cohomology

**Speaker:** Sara Venkatesh [Columbia University]

**Abstract:** Mirror symmetry predicts the existence of Floer invariants that yield local information about the Fukaya category. Guided by this, we construct a quantitative symplectic cohomology theory that detects Floer-essential Lagrangians within subdomains. This theory conjecturally specializes to a flavor of Rabinowitz Floer homology. We illustrate the quantitative behavior of this theory by examining negative line bundles over toric symplectic manifolds.

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Quantitative symplectic cohomology

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4:00pm Colloquium: Mohammed Abouzaid - Mirror symmetry, loop spaces, and immersed Lagrangians

**Where:** Math Tower P-131**When:** Thu, Apr 26 4:00pm — 5:00pm

**Title:** Mirror symmetry, loop spaces, and immersed Lagrangians

**Speaker:** Mohammed Abouzaid [Columbia University]

**Abstract:** A compelling approach to mirror symmetry, initiated by

Strominger-Yau-Zaslow and Fukaya, is to associate to a symplectic manifold with a Lagrangian torus fibration a mirror space consisting of the space of objects of the Fukaya category supported on the fibres with multiplicity one. In the simplest setting of the cotangent bundle of the torus, the mirror correspondence thus amounts to the natural identification between the group ring of the fundamental group and Laurent polynomials. I will begin by explaining how one can globalise this argument to yield a proof of homological mirror symmetry for manifolds admitting non-singular Lagrangian fibrations. Then I will explain how the main obstruction to generalise this proof is to formulate an appropriate notion of loop space for singular Lagrangians. Finally, I will sketch a construction that plays the role of the loop space for immersed Lagrangians, and indicate how this should suffice to prove mirror symmetry for examples arising from toric degenerations.

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Strominger-Yau-Zaslow and Fukaya, is to associate to a symplectic manifold with a Lagrangian torus fibration a mirror space consisting of the space of objects of the Fukaya category supported on the fibres with multiplicity one. In the simplest setting of the cotangent bundle of the torus, the mirror correspondence thus amounts to the natural identification between the group ring of the fundamental group and Laurent polynomials. I will begin by explaining how one can globalise this argument to yield a proof of homological mirror symmetry for manifolds admitting non-singular Lagrangian fibrations. Then I will explain how the main obstruction to generalise this proof is to formulate an appropriate notion of loop space for singular Lagrangians. Finally, I will sketch a construction that plays the role of the loop space for immersed Lagrangians, and indicate how this should suffice to prove mirror symmetry for examples arising from toric degenerations.

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2:00pm **YITP:** YITP seminar, Joel Meyers (CITA) [cosmology]

**When:** Fri, Apr 27 2:00pm — 3:00pm

Cosmological Probes of Fundamental Physics

Over the past few decades, cosmological surveys of the cosmic microwave background (CMB) and large scale structure have revolutionized our understanding of the universe at large, transforming cosmology into a precision science. In this talk, I will discuss the exciting scientific returns we expect from the next generation of cosmological observations. The improved sensitivity of upcoming CMB experiments will allow for fundamentally new insights into the very early universe and physics beyond the standard model. I will highlight some key theoretical targets and discuss the tools necessary to reach those goals.

Cosmological Probes of Fundamental Physics

Over the past few decades, cosmological surveys of the cosmic microwave background (CMB) and large scale structure have revolutionized our understanding of the universe at large, transforming cosmology into a precision science. In this talk, I will discuss the exciting scientific returns we expect from the next generation of cosmological observations. The improved sensitivity of upcoming CMB experiments will allow for fundamentally new insights into the very early universe and physics beyond the standard model. I will highlight some key theoretical targets and discuss the tools necessary to reach those goals.

2:30pm Dynamical Systems Seminar: Romain Dujardin - A closing lemma for polynomial automorphisms of $\mathbb{C}^2$

**Where:** Math Tower P-131**When:** Fri, Apr 27 2:30pm — 3:30pm

**Title:** A closing lemma for polynomial automorphisms of $\mathbb{C}^2$

**Speaker:** Romain Dujardin [Universit Pierre et Marie Curie]

**Abstract:** A basic and still open question in the dynamics of polynomial automorphisms of $\mathbb{C}^2$ is whether periodic saddle points are dense in the Julia set. In this talk I will explain the following

ergodic closing lemma: in the dissipative setting, the support of any invariant measure is (apart from a few obvious cases) contained in the closure of the set of saddle points.

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ergodic closing lemma: in the dissipative setting, the support of any invariant measure is (apart from a few obvious cases) contained in the closure of the set of saddle points.

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for more information please visit: http://scgp.stonybrook.edu/archives/20581

2:00pm **SCGP:** Weekly Physics Meetings: Saebyeok Jeong

**When:** Mon, Apr 30 2:00pm — 3:00pm

**Title:** Opers, surface defects, and Yang-Yang functional

2:00pm Thesis Defense: Dyi-Shing Ou - Nonexistence of Wandering Domains for Infinite Renormalizable H$\'e$non Maps

**Where:** Math Tower 5-127**When:** Mon, Apr 30 2:00pm — 3:00pm

**Title:** Nonexistence of Wandering Domains for Infinite Renormalizable H$\'e$non Maps

**Speaker:** Dyi-Shing Ou [Stony Brook University]

**Abstract:** In the thesis, I proved the absence of wandering domains for strongly dissipative infinitely renormalizable H$\'e$non-like maps with arbitrary stationary combinatorics. The theorem solves an open problem proposed by van Strien (2010) and Lyubich and Martens (2011). Unimodal maps are a reduced version of H$\'e$non-like maps in one-dimension and unimodal maps do not have wandering intervals. However, the classical proofs for unimodal maps break down in the H$\'e$non settings. To resolve this issue, two techniques, "the area argument" and "the good region and the bad region", are introduced in the thesis to prove the theorem.

The proof is split into two cases. The first case covers infinitely period-doubling renormalizable H$\'e$non-like maps. The second case covers infinitely renormalizable H$\'e$non-like maps with stationary combinatorics other than period-doubling. The difference between the proofs of the two cases is the way of how we measure the expansion of a set when it is iterated under a H$\'e$non-like map. The prior case relies on the Euclidean metric, and the later case relies on the hyperbolic metric. The two cases are disjoint, and together solve the problem for all stationary combinatorics.

As an application, the theorem helps us to understand the topological structure of the heteroclinic web: the union of the stable manifolds of the periodic points forms a dense set in the domain.

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The proof is split into two cases. The first case covers infinitely period-doubling renormalizable H$\'e$non-like maps. The second case covers infinitely renormalizable H$\'e$non-like maps with stationary combinatorics other than period-doubling. The difference between the proofs of the two cases is the way of how we measure the expansion of a set when it is iterated under a H$\'e$non-like map. The prior case relies on the Euclidean metric, and the later case relies on the hyperbolic metric. The two cases are disjoint, and together solve the problem for all stationary combinatorics.

As an application, the theorem helps us to understand the topological structure of the heteroclinic web: the union of the stable manifolds of the periodic points forms a dense set in the domain.

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4:00pm Algebraic geometry seminar: Cristian Minoccheri - 1-cycles and arithmetic of weighted complete intersections

**Where:** Math Tower P-131**When:** Mon, Apr 30 4:00pm — 5:00pm

**Title:** 1-cycles and arithmetic of weighted complete intersections

**Speaker:** Cristian Minoccheri [Stony Brook University]

**Abstract:** The geometry and arithmetic of Fano varieties are influenced by the geometry of low degree rational curves on them; for 2-Fano varieties (i.e. such that ch_2(X) is positive) this relation is even stronger. While no complete classification of 2-Fano varieties is known, many examples arise as low degree smooth weighted complete intersections, which include cyclic covers of projective space. I will discuss how, for this class of examples, the 2-Fano condition implies that the Chow group of 1-cycles is rather simple. I will also discuss how it implies that weighted complete intersections over function fields of curves satisfy a strong arithmetic property known as weak approximation at all places.

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4:00pm Geometry/Topology Seminar: Yann Rollin - TBA

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

**Title:** TBA

**Speaker:** Yann Rollin [University of Nantes]

**Abstract:**

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10:00am **SCGP:** Poisson Geometry Program Seminar: Dennis Sullivan

**Where:** SCGP 313**When:** Wed, May 2 10:00am — 12:00pm

**Title:**

1:00pm Graduate Student Seminar: Ying Hong Tham - TBA

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

**Title:** TBA

**Speaker:** Ying Hong Tham [Stony Brook University]

**Abstract:** TBA

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2:00pm **SCGP:** Poisson Geometry Program Seminar: Leon Takhtajan

**When:** Wed, May 2 2:00pm — 4:00pm

**Title:** “Some remarks on symplectic forms (in physics and mathematics)”

2:30pm Mini Course / Dynamics Learning Seminar: Dror Varolin - Solution of the Cauchy-Riemann Equations with $L^2$ estimates

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

**Title:** Solution of the Cauchy-Riemann Equations with $L^2$ estimates

**Speaker:** Dror Varolin [Stony Brook University]

**Abstract:** In this three-lecture mini-school we will explain the technique introduced by Hormander to obtain solutions, with $L^2$ estimates, for the inhomogeneous Cauchy-Riemann equations. We will then demonstrate several applications of the theorem and of the technique of its proof, with a focus on the construction of subharmonic functions with certain properties. The background needed is relatively elementary, consisting only basic real and complex analysis, and a little bit of the formalism of differential forms on manifolds (though the latter is not absolutely necessary).

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4:00pm Special Lectures: Graduate students - Graduate student recitals (1)

**Where:** P-131**When:** Wed, May 2 4:00pm — 5:30pm

**Title:** Graduate student recitals (1)

**Speaker:** Graduate students [Stony Brook University]

**Abstract:** 10-minute talks by some of our graduate students:

John Sheridan

Fangyu Zou

Aleksander Doan

Edward Bryden

Xuntao Hu

Yuhan Sun

Ruijie Yang

Benjamin Sokolowsky

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John Sheridan

Fangyu Zou

Aleksander Doan

Edward Bryden

Xuntao Hu

Yuhan Sun

Ruijie Yang

Benjamin Sokolowsky

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4:00pm Analysis Student Seminar: Matt Dannenberg - Intro to Stochastic Calculus

**Where:** Math Tower 5-127**When:** Wed, May 2 4:00pm — 5:00pm

**Title:** Intro to Stochastic Calculus

**Speaker:** Matt Dannenberg [Stony Brook University]

**Abstract:** We'll define what it means to integrate with respect to a stochastic process, such as Brownian motion. This gives us a formal way of understanding systems that behave randomly. After that, we will state a few of the main theorems and applications of this idea.

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10:00am **SCGP:** Poisson Geometry Program Seminar: Andras Szenes

**Where:** SCGP 313**When:** Thu, May 3 10:00am — 12:00pm

**Title:** An enumerative approach to the P=W conjecture for the moduli of Higgs bundles

**Abstract:** I will report on an enumerative approach to the P=W conjecture formulated by de Cataldo, Hausel and Migliorini. In joint work with Chiarello and Hausel, we develop a residue calculus for the equivariant intersection numbers on the moduli spaces of Higgs bundles, which leads to a proof of the conjecture for the rank-2 case (already shown by de Cataldo, Hausel and Migliorini with a completely different method).

2:00pm **SCGP:** Physics Seminar: Sasha Zhiboedov

**Where:** SCGP 313**When:** Thu, May 3 2:00pm — 3:00pm

**Title:** Finite Energy Sum Rules in CFTs

4:00pm Special Lectures: Graduate students - Graduate student recitals (2)

**Where:** P-131**When:** Thu, May 3 4:00pm — 5:00pm

**Title:** Graduate student recitals (2)

**Speaker:** Graduate students [Stony Brook University]

**Abstract:** 10-minute talks by some of our graduate students:

Selin Taşkent

Michael Albanese

Silvia Ghinassi

Mu Zhao

Zhongshan An

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Selin Taşkent

Michael Albanese

Silvia Ghinassi

Mu Zhao

Zhongshan An

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5:00pm **SCGP:** Opening Reception: Geometric Landscapes by Nikolay Bogoliubov

**When:** Thu, May 3 5:00pm — 6:00pm

10:00am **SCGP:** Poisson Geometry Program Seminar: Chenchang Zhu

**Where:** SCGP 313**When:** Fri, May 4 10:00am — 12:00pm

**Title:** Higher groups in higher gauge theory

**Abstract:** There has been much recent development on higher symmetries in topological orders as the study of topological phase of maters has become a very active field in condensed matter physics. In this talk, we will carry out the mathematical foundation of a recent joint project with Tian Lan and Xiao-Gang Wen in the above direction. Higher groups are group objects in a higher category. In a very concise way, they can be realised as a simplicial object satisfying suitable Kan conditions. We will give a more explicit algebraic model to realise some of them. This model is between the target of Dold-Kan functor and the skeleton case. Then we discuss higher gauge theory for topological orders, classification of them in lower dimensions, and explicit realisations in special cases.

2:30pm Dynamical Systems Seminar: Leonid Bunimovich - Finite Time Dynamics

**Where:** Math Tower P-131**When:** Fri, May 4 2:30pm — 3:30pm

**Title:** Finite Time Dynamics

**Speaker:** Leonid Bunimovich [Georgia Tech]

**Abstract:** Traditionally dynamical systems theory deals with asymptotic in time properties like ergodic theorems, mixing, etc, unless solutions are known and thus could be computed for any moment of time. Analogously probability theory deals with limit, i.e. again asymptotic in time, theorems. Moreover, all basic notions we use like Lyapunov exponents, entropies, various types of mixing involve taking a limit when time tends to infinity. I will demonstrate that some interesting finite time properties of "the most chaotic" dynamical systems can be rigorously studied. This direction of research appeared "by chance" in attempt to answer a traditional kind of question on dynamics which involves infinite time limit.

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Cinco de Mayo

**When:** Sat, May 5