- 9:30am - 10:30am

**Speaker:** Dongmin Gang

Title : Large N subleading corrections in AdS4/CFT3 using 3d-3d correspondence**Abstract:** 3d-3d correspondence studies 3d supersymmetric field theories obtained from M5-branes wrapped on 3-manifolds.

Using 3d-3d relations, various BPS partition functions of the 3d theories can be written in terms of invariants of complex Chern-Simons theories on the internal 3-manifolds. I will explain how the 3d-3d relations (combined with known mathematical results) help us to compute the large N behavior (including some subleading corrections) of the BPS partition functions. I will also discuss their holographic dual computations with emphasis on unsolved remaining issues.

- 2:30pm - 3:30pm

**Speaker:** Jonguk Yang, Stony Brook University**Title:** Polynomials with Bounded Type Siegel Disks**Abstract:** Consider a polynomial with a Siegel disc of bounded type rotation number. It is known that the Siegel boundary is a quasi-circle that contains at least one critical point. In the quadratic case, this means that the entire post-critical set is trapped within the Siegel boundary, where the theory of real analytic circle maps provides us with excellent control. However, in the higher degree case, there exist multiple critical points. A priori, these â€œfreeâ€ critical points may accumulate on the Siegel boundary in a complicated way, causing extreme distortions in the geometry nearby. In my talk, I show that in fact, this does not happen, and that the Julia set is locally connected at the Siegel boundary.

- 2:30pm - 3:30pm
- in zoom

**Title:** Polynomials with Bounded Type Siegel Disks **Speaker:** Jonguk Yang [Stony Brook University] **Abstract:** Consider a polynomial with a Siegel disc of bounded type rotation number. It is known that the Siegel boundary is a quasi-circle that contains at least one critical point. In the quadratic case, this means that the entire post-critical set is trapped within the Siegel boundary, where the theory of real analytic circle maps provides us with excellent control. However, in the higher degree case, there exist multiple critical points. A priori, these free critical points may accumulate on the Siegel boundary in a complicated way, causing extreme distortions in the geometry nearby. In my talk, I show that in fact, this does not happen, and that the Julia set is locally connected at the Siegel boundary.

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- 3:00pm - 4:15pm
- in Zoom

**Title:** A Fulton-Hansen theorem for almost homogeneous spaces **Speaker:** $\textbf{J\'anos}$ $\textbf{Koll\'ar}$ [Princeton University] **Abstract:** We prove a generalization of the Fulton-Hansen connectedness theorem, where projective space is replaced by a normal variety on which an algebraic group acts with a dense orbit. (joint with Aaron Landesman)

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- 4:45pm - 5:45pm
- in Zoom

**Title:** TBA **Speaker:** Fangyu Zou [Facebook] **Abstract:** Fangyu Zou is a machine learning engineer at Facebook, Inc. He graduated from the Math Department PhD program in 2019. In this talk, he will share his experience working as an engineer in a tech company, and how he prepared for getting such a job.

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- 9:00pm - 10:15pm
- in Zoom

**Title:** **Special time** On d-critical birational geometry and categorical DT theories **Speaker:** Yukinobu Toda [Kavli IPMU] **Abstract:** In this talk, I will explain an idea of analogue of birational geometry for Joyce's d-critical loci, and categorical Donaldson-Thomas theories on Calabi-Yau 3-folds. The motivations of this new framework include

categorifications of wall-crossing formulas of DT invariants and also giving a d-critical analogue of D/K conjecture in birational geometry. The main result is to realize the above story for local surfaces. I will show the window theorem for categorical DT theories on local surfaces and apply it to categorify wall-crossing invariance of genus zero GV invariants, MNOP/PT correspondence, etc.

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- 9:30am - 10:30am

**Title:** Higher derivative/subleading corrections to AdS Black hole entropy

Chairman: Jim Liu

Panelists: Kirill Hristov, Valentin Reys, Dongmin Gang and Alejandro Cabo-Bizet

- 1:00pm - 2:00pm

**Speaker:** Langte Ma**Title:** A SURGERY EXACT TRIANGLE IN SINGULAR INSTANTON HOMOLOGY**Abstract:** To an embedded knot K in an oriented 3-manifold Y , Kronheimer and Mrowka associated an invariant I^#(Y, K) by applying instanton Floer homology to a singular setting in their unknot-detector paper. In this talk, I will discuss an exact triangle in this homology which arises as performing surgery along the singular knot. I will first explain why such a triangle can be expected both in the chain level and homology level, then sketch a proof together with potential applications to 3-dimensional topology working in progress still.

- 4:30pm - 5:30pm
- in Online

**Title:** Induced subgraphs and tree decompositions **Speaker:** Maria Chudnovsky [Princeton University] **Abstract:** Tree decompositions are a powerful tool in structural graph theory, that is traditionally used in the context of forbidden graph minors. Connecting tree decompositions and forbidden induced subgraphs has so far remained out of reach. Recently we obtained several results in this direction; the talk will be a survey of these results.

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Last day to submit a Section/Credit Change Form to Office of Registrar.

- 11:00am - 12:00pm
- in Zoom

**Title:** TBA **Speaker:** Timothy Alland [Stony Brook University] **Abstract:** TBA

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- 2:30pm - 3:30pm

**Speaker:** Luna Lomonaco, IMPA, Rio de Janeiro**Title:** Mating quadratic maps with the modular group**Abstract:** Holomorphic correspondences are polynomial relations P(z,w)=0, which can be regarded as multi-valued self-maps of the Riemann sphere (implicit maps sending z to w). The iteration of such multi-valued map generates a dynamical system on the Riemann sphere (dynamical system which generalise rational maps and finitely generated Kleinian groups). We consider a specific 1-(complex)parameter family of (2:2) correspondences F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe dynamically. In particular, we show that for every a in the connectedness locus M_{Γ}, this family is a mating between the modular group and rational maps in the family Per_1(1); we develop for this family a complete dynamical theory which parallels the Douady-Hubbard theory of quadratic polynomials; and we show that M_{Γ} is homeomorphic to the parabolic Mandelbrot set M_1.

This is joint work with S. Bullett.

- 2:30pm - 3:30pm
- in zoom

**Title:** Mating quadratic maps with the modular group **Speaker:** Luna Lomonaco [IMPA, Rio de Janeiro] **Abstract:** Holomorphic correspondences are polynomial relations P(z,w)=0, which can be regarded as multi-valued self-maps of the Riemann sphere (implicit maps sending z to w). The iteration of such multi-valued map generates a dynamical system on the Riemann sphere (dynamical system which generalise rational maps and finitely generated Kleinian groups). We consider a specific 1-(complex)parameter family of (2:2) correspondences F_a (introduced by S. Bullett and C. Penrose in 1994), which we describe dynamically. In particular, we show that for every a in the connectedness locus M_{\Gamma}, this family is a mating between the modular group and rational maps in the family Per_1(1); we develop for this family a complete dynamical theory which parallels the Douady-Hubbard theory of quadratic polynomials; and we show that M_{\Gamma} is homeomorphic to the parabolic Mandelbrot set M_1.

This is joint work with S. Bullett.

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- 9:30am - 10:30am

**Speaker:** Dabholkar

- 1:00pm - 2:00pm

- 4:30pm - 5:30pm
- in Online

**Title:** Topological rigidity of the first Betti number and Ricci flow smoothing **Speaker:** Shaosai Huang [ University of Wisconsin-Madison] **Abstract:** The infranil fiber bundle is a typical structure appeared in the collapsing geometry with bounded sectional curvature. In this talk, I will discuss a topological condition on the first Betti numbers that guarantees a torus fiber bundle structure (a special type of infranil fiber bundle) for collapsing manifolds with only Ricci curvature bounded below. The main technique applied here is smoothing by Ricci flows. This covers my joint works with Bing Wang.

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- 9:30am - 10:30am

**Speaker:** Hosseini

- 2:30pm - 3:30pm

** Speaker: Michael Yampolsky**, University of Toronto

**Title:** TBA

- 2:30pm - 3:30pm
- in zoom

**Title:** mini-course: TBA **Speaker:** Michael Yampolsky [University of Toronto] **Abstract:** TBA

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- 3:00pm - 4:15pm
- in Zoom

**Title:** K3 surfaces: curves, sheaves, and moduli **Speaker:** Rahul Pandharipande [ETH $\text{Z\"urich}$ ] **Abstract:** I will talk about some results and open questions related

to the moduli of maps of curves to K3 surfaces, sheaves

on K3 surfaces, and moduli of K3 surfaces themselves.

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- 6:00pm - 7:00pm
- in Zoom

**Title:** TBA **Speaker:** Joseph Thurman [Goldman Sachs] **Abstract:** TBA

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- 1:00pm - 2:00pm

- 4:30pm - 5:30pm
- in Online

**Title:** Primes in arithmetic progressions: The Riemann Hypothesis - and beyond! **Speaker:** James Maynard [Oxford University] **Abstract:** One of the oldest problems about prime numbers is asking how many primes there are of a given size in an arithmetic progression. Dirichlet's famous theorem shows that there are large primes in any progression unless there is an obvious reason why not, but more refined questions lead quickly to statements equivalent to versions of the Riemann Hypothesis, which unfortunately remains unsolved.

We can prove that the Generalized Riemann Hypothesis is true 'on average', and this can often be used as an unconditional substitute for the Riemann Hypothesis. I'll introduce these ideas and mention some recent work about primes in arithemetic progressions which 'breaks the 1/2 barrier' and shows that something *stronger* that the Riemann Hypothesis holds on average.

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