Easter Sunday

**When:** Sun, Apr 21

Easter Monday

**When:** Mon, Apr 22

11:30am **YITP:** Cosmo seminar: Enea Di Dio

**Where:** ESS 450**When:** Mon, Apr 22 11:30am — 12:30pm

**Speaker:** Enea Di Dio

**Title:** Relativistic effects and gravitational redshift on LSS

**Abstract:**

The next generation of LSS surveys will probe almost the whole observable universe at late time. To correctly interpret measurements of modes at the horizon scale we need to develop an accurate gauge-invariant description of LSS.

In my talk I will present the relativistic description of Large Scale Structure observables, by investigating the relevance of such corrections beyond the Newtonian description. In particular, I will show how to use cross-correlations as a "smoking gun" for relativistic effects detection and how such corrections could potentially contaminate primordial non-gaussianity measurements.

Finally, I will show how to extend perturbation theory within a relativistic framework and how this affects the interpretation of gravitational redshift measurements.

The next generation of LSS surveys will probe almost the whole observable universe at late time. To correctly interpret measurements of modes at the horizon scale we need to develop an accurate gauge-invariant description of LSS.

In my talk I will present the relativistic description of Large Scale Structure observables, by investigating the relevance of such corrections beyond the Newtonian description. In particular, I will show how to use cross-correlations as a "smoking gun" for relativistic effects detection and how such corrections could potentially contaminate primordial non-gaussianity measurements.

Finally, I will show how to extend perturbation theory within a relativistic framework and how this affects the interpretation of gravitational redshift measurements.

4:00pm Special Colloquium: David Sondak - Machine Learning, Fluid Mechanics, and Turbulence

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

**Title:** Machine Learning, Fluid Mechanics, and Turbulence

**Speaker:** David Sondak [Institute for Applied Computational Science, Harvard University]

**Abstract:** Fluids pervade every aspect of human life and beyond from the biological through the geophysical and up to the astrophysical. Moreover, most flows interest are in a state of turbulence, which is highly irregular with multiple interacting scales feeding off of each other. Given the ubiquity of turbulence in nature, scientists and engineers must be able to make predictions of systems that are either influenced by turbulence or in a state of turbulence themselves. The multiscale nature of turbulence poses considerable mathematical and numerical challenges. Finding reduced models that capture essential physics while retaining predictive power is of utmost importance. This talk will begin with an introduction to fluid mechanics and its significance while providing some intuition on multiscale phenomena. Following this, the classical problem of turbulence modeling will be discussed in the context of the Reynolds-Averaged Navier Stokes (RANS) equations. A brief machine learning interlude will be followed by its application to learning closure models for the RANS equations. A study of the predictions and behavior of a deep neural network, which preserves key physical constraints of the model, will be presented. Extensions of this neural network model to embed the nonlocality of RANS models will be discussed. The talk will close with a discussion of unsupervised machine learning approaches for turbulence and future directions.

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4:15pm **SCGP:** Physics Colloquium: Netta Engelhardt

**Where:** Harriman 137**When:** Tue, Apr 23 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/

1:00pm Math Club: Joe Mitchel - Geometric Optimization Problems for Efficient Viewing: Finding Good Ways to See Things Well

**Where:** Physics P-116**When:** Wed, Apr 24 1:00pm — 2:30pm

**Title:** Geometric Optimization Problems for Efficient Viewing: Finding Good Ways to See Things Well

**Speaker:** Joe Mitchel [Stony Brook University]

**Abstract:** A famous problem posed by Victor Klee in the early 1970's is the Art Gallery Problem: How many points ("guards") are sufficient to place within a simple polygon $P$ having $n$ vertices so that every point of $P$ is "seen" by at least one guard? This problem falls into a rich class of computational geometry problems that ask one to optimally cover a domain. We discuss several interesting mathematical and algorithmic questions that arise in this class, both in the case of stationary guards and mobile robotic guards. The problems are simple to state, easy to visualize, but often very challenging to solve.

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2:00pm **SCGP:** Physics Seminar: Netta Engelhardt

**Where:** SCGP 313**When:** Wed, Apr 24 2:00pm — 3:00pm

**Title:** On the Road to Cosmic Censorship: the Penrose Inequality in AdS/CFT

**Abstract:** I will give a holographic argument in favor of the AdS Penrose inequality, which conjectures a lower bound on the total mass in terms of the area of apparent horizons. This inequality is often viewed as a test of cosmic censorship. Time permitting, I’ll also discuss a generalization to charged black holes and connections with a quasi-local energy and the second law for apparent horizons.

2:30pm Mini Course / Dynamics Learning Seminar: Saeed Zakeri - Cyclic permutations, periodic orbits and complex polynomials

**Where:** Math Tower P-131**When:** Wed, Apr 24 2:30pm — 3:30pm

**Title:** Cyclic permutations, periodic orbits and complex polynomials

**Speaker:** Saeed Zakeri [CUNY]

**Abstract:** There is a well-known connection between the dynamics of complex polynomial maps of degree $k \geq 2$ and the multiplication-by-$k$ map $m_k(x) = kx$ (mod 1) acting on the circle at infinity. Motivated by this link, we study the combinatorial types of periodic orbits of $m_k$ and the frequency with which they occur. In fact, for every $q$-cycle $\sigma$ in the permutation group $S_q$ we give a full description of the set of period $q$ orbits of $m_k$ that realize $\sigma$ and count how many such orbits there are. The description is based on an invariant called the ``fixed point distribution'' vector and is achieved by reducing the realization problem to finding the stationary state of an associated Markov chain. This is joint work with C. L. Petersen.

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3:30pm **YITP:** Pheno seminar: Alexander Turbiner (ICN-UNAM and Stony Brook University). Choreography in Physics, in (non)-Newtonian gravity

**When:** Wed, Apr 24 3:30pm — 4:30pm

By definition the choreography (dancing curve) is the trajectory on which n classical bodies move chasing each other without collisions. The first choreography (the Remarkable Figure Eight) at zero angular momentum was discovered unexpectedly by C Moore (Santa Fe Institute) at 1993 for 3 equal masses in R3 Newtonian gravity numerically. At the moment about 6,000 choreographies are known, all numerically, in Newtonian gravity. Will GR support such choreographies? Some number of 3-body choreographies is known for Lennard- Jones potential (hence, relevant for molecular physics) and for some other potentials again numerically; it might be proved their existence for quarkonia potential, thus, for baryons.

Does exist (non)-Newtonian gravity for which dancing curve is known analytically? - Yes, a single example is known - it is algebraic lemniscate by Jacob Bernoulli (1694) - and it will be a concrete subject of the talk. Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate with χ2 deviation 10−7. Both choreographies admit any odd numbers of bodies on them. 3-body choreography on lemniscate defines maximally superintegrable trajectory.

Talk will be accompanied by numerous animations.

By definition the choreography (dancing curve) is the trajectory on which n classical bodies move chasing each other without collisions. The first choreography (the Remarkable Figure Eight) at zero angular momentum was discovered unexpectedly by C Moore (Santa Fe Institute) at 1993 for 3 equal masses in R3 Newtonian gravity numerically. At the moment about 6,000 choreographies are known, all numerically, in Newtonian gravity. Will GR support such choreographies? Some number of 3-body choreographies is known for Lennard- Jones potential (hence, relevant for molecular physics) and for some other potentials again numerically; it might be proved their existence for quarkonia potential, thus, for baryons.

Does exist (non)-Newtonian gravity for which dancing curve is known analytically? - Yes, a single example is known - it is algebraic lemniscate by Jacob Bernoulli (1694) - and it will be a concrete subject of the talk. Astonishingly, Newtonian Figure Eight coincides with algebraic lemniscate with χ2 deviation 10−7. Both choreographies admit any odd numbers of bodies on them. 3-body choreography on lemniscate defines maximally superintegrable trajectory.

Talk will be accompanied by numerous animations.

4:00pm Algebraic geometry seminar: Valery Alexeev - Degenerations of K3 surfaces and 24 points on the sphere

**Where:** Math Tower P-131**When:** Wed, Apr 24 4:00pm — 5:30pm

**Title:** Degenerations of K3 surfaces and 24 points on the sphere

**Speaker:** Valery Alexeev [University of Georgia]

**Abstract:** I will discuss Kulikov and stable degenerations of K3 surfaces and describe explicit, geometric compactifications of their moduli spaces in several interesting cases. Based on joint work with Philip Engel and Alan Thompson.

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1:00pm **SCGP:** Hitchin Systems Program Seminar: Andres Collinucci

**Where:** SCGP 313**When:** Thu, Apr 25 1:00pm — 2:30pm

1:00pm Symplectic Geometry Seminar: Kenji Fukaya - Floer homology of noncompact Lagrangian submanifolds in the divisor complement.

**Where:** Math Tower 5-127**When:** Thu, Apr 25 1:00pm — 2:00pm

**Title:** Floer homology of noncompact Lagrangian submanifolds in the divisor complement.

**Speaker:** Kenji Fukaya [SCGP]

**Abstract:** This is a part of the project to study Lagrangian Floer theory in the divisor complement. In my previous paper with A. Daemi, we studied the case of compact Lagrangian sub manifolds and showed, roughly speaking, the story is the same as the case of compact symplectic manifolds. In this talk I will discuss the case of noncompact Lagrangian sub manifolds. Some new phenomenon appears.

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2:30pm **YITP:** Cosmo seminar: Katerina Chatziioannou (CCA)

**When:** Thu, Apr 25 2:30pm — 3:30pm

2:30pm Analysis Seminar: Vladimir Bozin - Quasiconformal harmonic maps and the bi-Lipschitz condition

**Where:** P-131**When:** Thu, Apr 25 2:30pm — 3:30pm

**Title:** Quasiconformal harmonic maps and the bi-Lipschitz condition

**Speaker:** Vladimir Bozin [University of Belgrade]

**Abstract:** We discuss some recent results regarding the Euclidean quasiconformal harmonic maps. In particular, we show, using the Gehring-Osgood inequality, that quasiconformal maps between plane domains with $C^{1,\alpha}$ boundary are bi-Lipschitz. We will also discuss questions related to the boundary behavior of hqc maps and generalizations to the higher dimensional case.

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4:00pm Colloquium: John Morgan - An integral structure in quantum cohomology and a monodromy conjecture of Morrison for families of Calabi-Yau manifolds

**Where:** Math Tower P-131**When:** Thu, Apr 25 4:00pm — 5:00pm

**Title:** An integral structure in quantum cohomology and a monodromy conjecture of Morrison for families of Calabi-Yau manifolds

**Speaker:** John Morgan [SCGP]

**Abstract:**

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11:00am Thesis Defense: Fangyu Zou - Monge-Ampre equation on the complement of a divisor

**Where:** Physics P-129**When:** Fri, Apr 26 11:00am — 12:00pm

**Title:** Monge-Ampre equation on the complement of a divisor

**Speaker:** Fangyu Zou [Stony Brook University]

**Abstract:** In this dissertation we discuss two seperate topics. In the first part we consider the complex Monge-Ampère equation on complete Kähler manifolds with cusp singularity along a divisor when the right hand side $F$ has rather weak regularity. We prove a compactness result on the solutions to a $\varepsilon$-perturbed equation of the Monge-Ampère equation when the right hand side $F$ is in some *weighted* $W^{1,p_0}$ space for $p_0 > 2n$ where $n$ is the complex dimension. As an application we show that there exists a classical $W^{3,p_0}$ solution for complex Monge-Ampère equation when $F$ is in the weighted $W^{1,p_0}$. The key ingredient lies in using the de Giorgi-Nash-Moser theory to derive the uniform estimates of the gradient $\nabla \varphi_\varepsilon$ and the Laplacian $\Delta \varphi_\varepsilon$ in terms of the weighted $W^{1,p_0}$ norm of $F$.

In the second part we consider the Chern-Yamabe problem of finding constant Chern scalar curvature metrics in the conformal classes. We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.

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In the second part we consider the Chern-Yamabe problem of finding constant Chern scalar curvature metrics in the conformal classes. We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.

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2:00pm Thesis Defense: Zhongshan An - Ellipticity of Bartnik Boundary Data for Stationary Vacuum Spacetimes

**Where:** Physics P-123**When:** Fri, Apr 26 2:00pm — 3:00pm

**Title:** Ellipticity of Bartnik Boundary Data for Stationary Vacuum Spacetimes

**Speaker:** Zhongshan An [Stony Brook University]

**Abstract:** The Bartnik quasi-local mass is defined to measure the mass of a bounded manifold with boundary, where a collection of geometric boundary data - the so called Bartnik boundary data - plays a key role. Bartnik proposed the open problem whether there exist stationary vacuum metrics on a given manifold with fixed Bartnik boundary data. To answer this question, it is important to prove the ellipticity of Bartnik boundary data for stationary vacuum metrics.

We establish a moduli space of stationary vacuum metrics which admits manifold structure, and then set up a well-defined boundary map in the moduli space, assigning a metric class with its Bartnik boundary data. Furthermore, we prove the boundary map is Fredholm by showing that the stationary vacuum equations (combined with proper gauge terms) and the Bartnik boundary conditions form an elliptic boundary value problem. As an application, we prove that locally, the Bartnik boundary data near the standard flat one can be realized by a unique (up to diffeomorphism) stationary vacuum metric.

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We establish a moduli space of stationary vacuum metrics which admits manifold structure, and then set up a well-defined boundary map in the moduli space, assigning a metric class with its Bartnik boundary data. Furthermore, we prove the boundary map is Fredholm by showing that the stationary vacuum equations (combined with proper gauge terms) and the Bartnik boundary conditions form an elliptic boundary value problem. As an application, we prove that locally, the Bartnik boundary data near the standard flat one can be realized by a unique (up to diffeomorphism) stationary vacuum metric.

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2:30pm Dynamical Systems Seminar: Saeed Zakeri - On the correspondence of external rays under renormalization

**Where:** Math Tower P-131**When:** Fri, Apr 26 2:30pm — 3:30pm

**Title:** On the correspondence of external rays under renormalization

**Speaker:** Saeed Zakeri [CUNY]

**Abstract:** In a recent joint work with C. L. Petersen, we investigate the set of (smooth or broken) external rays that accumulate on a non-degenerate periodic component of a polynomial Julia set. This work can be viewed as a complement to the well-studied case of connected Julia sets initiated by Douady and Hubbard in the late 1980's.

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4:00pm Geometric Analysis Learning Seminar: Yu Li - Almost flat manifolds

**Where:** P-131 Math Tower**When:** Fri, Apr 26 4:00pm — 6:00pm

**Title:** Almost flat manifolds

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

**Abstract:** Gromov's theorem on almost flat manifolds is the cornerstone for the collapsing theory with bounded sectional curvature. In this talk, I will discuss the proof of the theorem that any almost flat closed manifold is diffeomorphic to an infranilmanifold of finite index.

Reference: Gromov, M- Almost flat manifolds; Peter Buser & Hermann Karcher, Gromov's Almost Flat Manifolds

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Reference: Gromov, M- Almost flat manifolds; Peter Buser & Hermann Karcher, Gromov's Almost Flat Manifolds

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For more information please visit: http://scgp.stonybrook.edu/archives/25455

2:30pm **SCGP:** Weekly Physics Meeting: Zohar Komargodski

**Where:** 313**When:** Mon, Apr 29 2:30pm — 3:30pm