Presidents' Day (regional holiday)

**When:** Mon, Feb 19

Public holiday in: Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, District of Columbia, Florida, Hawaii, Idaho, Illinois, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New York, North Dakota, Northern Mariana Islands, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wyoming

Public holiday in: Alabama, Alaska, Arizona, Arkansas, California, Colorado, Connecticut, District of Columbia, Florida, Hawaii, Idaho, Illinois, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New York, North Dakota, Northern Mariana Islands, Ohio, Oklahoma, Oregon, Pennsylvania, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virginia, Washington, West Virginia, Wyoming

1:00pm Grad / Postdoc Professional Development Seminar: No seminar - No seminar

**Where:** Math Tower P-131**When:** Mon, Feb 19 1:00pm — 2:30pm

**Title:** No seminar

**Abstract:** No seminar due to President Stanley's visit.

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2:00pm **SCGP:** Weekly Physics Meetings: Connor Behan

**Where:** SCGP 313**When:** Mon, Feb 19 2:00pm — 3:00pm

**Title:** CFT data on conformal manifolds

1:00pm **SCGP:** SCGP Weekly Talk - Marek Karliner

**When:** Tue, Feb 20 1:00pm — 2:00pm

**Title:** The Social Life of Heavy Quarks

11:30am RTG Seminar: Yoonjoo Kim - The Hilbert-Mumford Criterion for Stability

**Where:** 5-127**When:** Wed, Feb 21 11:30am — 12:30pm

**Title:** The Hilbert-Mumford Criterion for Stability

**Speaker:** Yoonjoo Kim [Stony Brook University]

**Abstract:** In this talk we will focus our attention on the notion of stability previously introduced for these actions by reductive groups. We will state a theorem, due in part to Hilbert and Mumford respectively, which detects the (semi)stable points of an action using an eigenanalysis of the 1-parameter subgroups, complete with examples.

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1:00pm Graduate Student Seminar: Prithviraj Chowdhury - TBA

**Where:** Math Tower P-131**When:** Wed, Feb 21 1:00pm — 2:00pm

**Title:** TBA

**Speaker:** Prithviraj Chowdhury [Stony Brook University]

**Abstract:** TBA

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1:30pm **SCGP:** Physics Seminar: Austin Joyce

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

**Title:** Spin-2 scattering amplitudes and asymptotic superluminality

2:30pm Mini Course / Dynamics Learning Seminar: Babak Modami - Minimal nonuniquely ergodic foliations on surfaces: I

**Where:** Math Tower P-131**When:** Wed, Feb 21 2:30pm — 3:30pm

**Title:** Minimal nonuniquely ergodic foliations on surfaces: I

**Speaker:** Babak Modami [Stony Brook University]

**Abstract:** Measured foliations (laminations) on surfaces are well-known examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichm\"uller and Weil-Petersson geodesics in the Teichm\"uller space.

In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations.

This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichm\"uller space (which won't be discussed in the minicourse).

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In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations.

This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichm\"uller space (which won't be discussed in the minicourse).

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4:00pm Algebraic geometry seminar: Jian Xiao - Local positivity for curves

**Where:** Math Tower P-131**When:** Wed, Feb 21 4:00pm — 5:30pm

**Title:** Local positivity for curves

**Speaker:** Jian Xiao [Northwestern]

**Abstract:** One of the most important invariants measuring the local positivity of a nef line bundle is the local Seshadri function introduced by Demailly. We first give a brief introduction to this invariant. Then using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants, studied also independently by M. Fulger, have nice properties similar to those for divisors. In particular, this enables us to obtain a Seshadri type ampleness criterion for movable curves, and give a characterization of the divisorial components of the non-ample locus of a big class. (Joint work with N. McCleerey.)

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1:00pm Symplectic Geometry Seminar: Yuhan Sun - Finding nondisplaceable Lagrangian tori via toric degeneration.

**Where:** Math Tower 5-127**When:** Thu, Feb 22 1:00pm — 2:00pm

**Title:** Finding nondisplaceable Lagrangian tori via toric degeneration.

**Speaker:** Yuhan Sun [Stony Brook University]

**Abstract:** Starting with a semi-Fano toric surface, I will explain how to find families of Lagrangian tori with nontrivial deformed Floer cohomology. The proof uses toric degeneration method to compute the potential functions of these tori.

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2:30pm **YITP:** Pheno seminar: Prateek Agrawal (Harvard). "The strong CP problem and UV instantons"

**When:** Thu, Feb 22 2:30pm — 3:30pm

The absence of sizeable CP violation in the strong sector is a long standing puzzle. A class of solutions to this problem rely on a global U(1) symmetry that is anomalous with QCD. These solutions lead to robust low-energy predictions, for example a massless up quark or a light axion. I will present simple extensions to such solutions which can dramatically change these low-energy predictions. In our models, contributions from small instantons play a significant role in affecting the low-energy physics while preserving the solution to the strong CP problem.

The absence of sizeable CP violation in the strong sector is a long standing puzzle. A class of solutions to this problem rely on a global U(1) symmetry that is anomalous with QCD. These solutions lead to robust low-energy predictions, for example a massless up quark or a light axion. I will present simple extensions to such solutions which can dramatically change these low-energy predictions. In our models, contributions from small instantons play a significant role in affecting the low-energy physics while preserving the solution to the strong CP problem.

4:00pm Colloquium: Nets Katz - Semialgebraic sets and the Kakeya Problem

**Where:** Math Tower P-131**When:** Thu, Feb 22 4:00pm — 5:00pm

**Title:** Semialgebraic sets and the Kakeya Problem

**Speaker:** Nets Katz [Caltech]

**Abstract:** In joint work with Keith Rogers, we study the connection between the Kakeya problem and the highlights of the theory of semialgebraic sets such as Tarski's projection theorem and Gromov's algebraic lemma.

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2:30pm Student Algebraic Geometry Seminar: Sasha Victorova - Canonical models, minimal models and their singularities

**Where:** Math Tower 5-127**When:** Fri, Feb 23 2:30pm — 3:30pm

**Title:** Canonical models, minimal models and their singularities

**Speaker:** Sasha Victorova [Stony Brook University]

**Abstract:** In this talk we will run with the definitions of canonical and terminal singularities from last week and use them to give definitions of canonical and minimal models of (quasi-)projective varieties. As usual we will turn to examples to motivate the main ideas.

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2:30pm Dynamical Systems Seminar: Zhiqiang Li - Prime orbit theorems for expanding Thurston maps

**Where:** Math Tower P-131**When:** Fri, Feb 23 2:30pm — 3:30pm

**Title:** Prime orbit theorems for expanding Thurston maps

**Speaker:** Zhiqiang Li [Stony Brook University]

**Abstract:** Analogues of the Riemann zeta function were first introduced into geometry by A. Selberg and into dynamics by M. Artin, B. Mazur, and S. Smale. Analytic studies of such dynamical zeta functions yield quantitative information on the distribution of closed geodesics and periodic orbits.

We obtain the first Prime Orbit Theorem, as an analogue of the Prime Number Theorem, in complex dynamics outside of hyperbolic maps, for a class of branched covering maps on the $2$-sphere called expanding Thurston maps $f$. More precisely, we show that the number of primitive periodic orbits of $f$, ordered by a weight on each point induced by a non-constant real-valued H\"{o}lder continuous function on $S^2$ satisfying some additional regularity conditions, is asymptotically the same as the well-known logarithmic integral, with an exponentially small error term. Such a result follows from our quantitative study of the holomorphic extension properties of the associated dynamical zeta functions and dynamical Dirichlet series.

In particular, the above result applies to postcritically-finite rational maps whose Julia set is the whole Riemann sphere. Moreover, we prove that the regularity conditions needed here are generic; and for a Latt\`{e}s map $f$, a continuously differentiable function satisfies such a condition if and only if it is not cohomologous to a constant. This is a joint work with T. Zheng.

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We obtain the first Prime Orbit Theorem, as an analogue of the Prime Number Theorem, in complex dynamics outside of hyperbolic maps, for a class of branched covering maps on the $2$-sphere called expanding Thurston maps $f$. More precisely, we show that the number of primitive periodic orbits of $f$, ordered by a weight on each point induced by a non-constant real-valued H\"{o}lder continuous function on $S^2$ satisfying some additional regularity conditions, is asymptotically the same as the well-known logarithmic integral, with an exponentially small error term. Such a result follows from our quantitative study of the holomorphic extension properties of the associated dynamical zeta functions and dynamical Dirichlet series.

In particular, the above result applies to postcritically-finite rational maps whose Julia set is the whole Riemann sphere. Moreover, we prove that the regularity conditions needed here are generic; and for a Latt\`{e}s map $f$, a continuously differentiable function satisfies such a condition if and only if it is not cohomologous to a constant. This is a joint work with T. Zheng.

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1:00pm Grad / Postdoc Professional Development Seminar: Robert Lazarsfeld - Robert's rules of publishing

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

**Title:** Robert's rules of publishing

**Speaker:** Robert Lazarsfeld [Stony Brook University]

**Abstract:**

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2:00pm **SCGP:** Weekly Physics Meetings: Zohar Komargodski

**When:** Mon, Feb 26 2:00pm — 3:00pm

5:30pm First and Second Year Student Seminar: David Ebin - TBA

**Where:** Math Tower 5-127**When:** Tue, Feb 27 5:30pm — 6:30pm

**Title:** TBA

**Speaker:** David Ebin [Stony Brook University]

**Abstract:**

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