- 4:00pm - 5:00pm
- in Math P-131

**Title:** Intersections of Local Cohomology and Hodge Theory **Speaker:** Scott Hiatt [Purdue University] **Abstract:** Introduced by Grothendieck, Local Cohomology has become a valuable tool in commutative algebra, and has many applications in Algebraic Geometry. In this talk, we will use the theories of Local Cohomology with Hodge Theory to study Hodge structures and differential forms on singular and quasi-projective varieties.

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- 10:00am - 12:00pm
- in SCGP 313

Speakers: Tere Seara, Pau Martin and Rafael Ramirez-Ros (Universitata Politecnica de Catalunya, Spain)**Title:** Exponentially small phenomena in analytic convex billiards

- 1:00pm - 2:30pm
- in Math P-430

**Title:** TBA **Speaker:** Abhishek Mallick [Rutgers University] **Abstract:**

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Last day for Fall/Winter degree candidates to apply for graduation via SOLAR. Applications submitted after 11/9/22 will not appear in the commencement publication.

- 10:30am - 11:30am

**Speaker:** Marco Lenci (Università degli Studi di Bologna, Italy)**Title:** Exactness and K-mixing for extensions of dynamical systems, with application to periodic Lorentz gases**Abstract:** Exactness and the K-property (a.k.a. K-mixing) are strong ergodic properties whose significance is that a dynamical system progressively loses all information about its initial conditions. These properties were the subject of intense investigation in the second half of last century before being somewhat superseded by the stronger Bernoulli property, which was at the time proved for a number of popular systems, including many billiards. But the Bernoulli property can only be formulated for dynamical systems preserving a finite measure, while exactness and the K-property work equally well in infinite-measure contexts, which partly explains a revived interest in them.

I will present some recent general theorems on the exact or K decomposition of extensions of exact or K dynamical systems. One immediate application is that, in large generality, a recurrent periodic Lorentz gas whose finite-measure factor is proved to be hyperbolic is K-mixing. This includes virtually all previously studied 2-dimensional periodic Lorentz gases and d-dimensional periodic Lorentz tubes, as well as many d-dimensional periodic Lorentz slabs.

Joint work with Daniele Galli.

- 2:30pm - 3:30pm
- in Math P-131

**Title:** Real bimodal quadratic rational maps: moduli space and entropy (with K. Filom and S. Kang) **Speaker:** Kevin Pilgrim [Indiana University Bloomington] **Abstract:** Bruin-van Strien and Kozlovski showed that for multimodal

self-maps $f$ of the unit interval, the function $f \mapsto h(f)$

sending $f$ to its topological entropy is monotone. K. Filom and I

showed that for interval maps arising from real bimodal quadratic

rational maps, this monotonicity fails. A key ingredient in our proof

is an analysis of a family $f_{p/q}, p/q \in \mathbb{Q}/\mathbb{Z}$ of

critically finite maps on which the dynamics on the postcritical set

is conjugate to the rotation $x \mapsto x+p b \mod q$ on

$\mathbb{R}/\mathbb{Z}$, where $x=0$ and $x=1$ correspond to the two

critical points. The recent PhD thesis of S. Kang constructs a

piecewise-linear (PL) copy of the well-known Farey tree whose vertices are expanding PL quotients of the $f_{p/q}$'s. This PL model, conjecturally, sheds light on the moduli space of the real quadratic bimodal family, and on the variation of entropy among such maps.

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- 10:30am - 12:00pm
- in Math P-131

**Title:** Invariants of Real Vector Bundles **Speaker:** Jiahao Hu [Stony Brook University] **Abstract:** For a compact smooth manifold with corners (or finite CW-complex) X, we can prescribe a finite set of spin or $spin^h$ manifolds (possibly with boundary) mapping into it so that every real vector bundle over X is determined, up to stable equivalence, by the Dirac indices of the real vector bundle when pulled-back onto those prescribed spin or $spin^h$ manifolds. Our proof features a thorough study of indices of Dirac operators on $spin^h$ manifolds and a general duality between cycles and cocycles. Dissertation Advisor: Dennis Sullivan

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- 1:00pm - 2:00pm
- in Math P-131

**Title:** TBD **Speaker:** Tarek Elgindi [Duke University] **Abstract:** Please note the special day and time

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- 4:00pm - 5:00pm
- in Math 5-127

**Title:** TBA **Speaker:** Chris Bishop [Stony Brook University] **Abstract:**

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- 10:00am - 12:00pm
- in SCGP 313

**Speaker:** Alexey Glutsuyk (CNRS & ENS Lyon)**Title:** On algebraically integrable planar, dual and projective billiards

- 1:15pm - 2:15pm
- in 102

**Title:** On the Formation of Coherent Structures in Ideal Fluids**Abstract:** We will discuss recent ideas and results related to the formation and dynamics of coherent structures in ideal fluids. The study of such structures has had a profound impact on many fundamental problems in the study of the incompressible Euler equation. As a first example, we will discuss self-similar solutions; these are three-dimensional flows that exactly self-enhance all the way to a finite-time singularity. Self-similar solutions have been shown to attract nearby solutions to become singular as well. We will also discuss coherent structures in two dimensions, which play an important role in the infinite-time relaxation of solutions despite the conservative nature of the equations.

- 2:30pm - 3:30pm
- in SCGP 313

*Mini-course by Gregory Falkovich*

September 26 - November 28, 2023 on Tuesdays at 2:30pm in room 313

** Title: ** Introduction to Information Theory

**Selected Subjects: **

Measuring Uncertainty

Mutual Information and Entanglement Entropy, Redundancy of Language and Genetic Code

Information is Life and Money

Theory of Mind – Active Inference

Information in Quantum Mechanics and Statistics

- 4:00pm - 5:30pm
- in Math P-131

**Title:** ADM mass for $C^0$ metrics and distortion under Ricci-DeTurck flow **Speaker:** Paula Burkhardt-Guim [NYU] **Abstract:** We show that there exists a quantity, depending only on $C^0$ data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the $C^0$ sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the $C^0$ mass at infinity is independent of choice of $C^0$-asymptotically flat coordinate chart, and the $C^0$ local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.

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- 2:00pm - 3:00pm
- in SCGP 313

- 2:30pm - 3:30pm
- in Math P-131

**Title:** TBA **Speaker:** Insung Park [Stony Brook University] **Abstract:**

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- 4:00pm - 5:30pm
- in Math P-131

**Title:** Complexes of stable birational invariants **Speaker:** James Hotchkiss [Columbia University] **Abstract:** In the study of the rationality problem, a common situation is that one has a smooth variety degenerating to a singular one, and one wishes to find computable invariants of the special fiber which obstruct the rationality of the general fiber. I will explain a general procedure for constructing such invariants. As an application, A^1-connectedness specializes in smooth families. Joint with David Stapleton.

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- 10:00am - 12:00pm
- in SCGP 313

**Speaker:** Alexey Glutsuyk (CNRS & ENS Lyon)**Title:** On algebraically integrable planar, dual and projective billiards

- 1:00pm - 2:30pm
- in Math 4-130

**Title:** TBA **Speaker:** Vukasin Stojisavljevic [CRM, Universite de Montreal] **Abstract:**

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