For more information please visit: http://scgp.stonybrook.edu/archives/28586

2:30pm **YITP:** Philip Armitage (SBU)

**Where:** Math building 6125**When:** Thu, Sep 19 2:30pm — 3:30pm

**Title:** "Open problems in planet formation"

**Abstract:**

The formation and stability of the Solar System are classical problems that exercised Newton, Laplace, Poincare, and many others over the years. Following the discovery of the first extrasolar planets in 1995, it has become ever more clear that many planetary systems - including the most common examples - look qualitatively different from the Solar System, and this has prompted new thinking as to how planetary systems form and evolve. In this talk, I will give a brief overview of what we now know about the initial conditions and outcome of the planet formation process, and how we understand the physics at a back-of-the-envelope level. I will then discuss some open theoretical problems, and directions that we are pursuing to address them.

The formation and stability of the Solar System are classical problems that exercised Newton, Laplace, Poincare, and many others over the years. Following the discovery of the first extrasolar planets in 1995, it has become ever more clear that many planetary systems - including the most common examples - look qualitatively different from the Solar System, and this has prompted new thinking as to how planetary systems form and evolve. In this talk, I will give a brief overview of what we now know about the initial conditions and outcome of the planet formation process, and how we understand the physics at a back-of-the-envelope level. I will then discuss some open theoretical problems, and directions that we are pursuing to address them.

3:30pm **SCGP:** Quantum Mechanical Systems Program Seminar: David Pirtskhalava

**Where:** 313**When:** Thu, Sep 19 3:30pm — 4:30pm

**Title:** Field Theory for Quantum Matter in Dwarf Stars

**Abstract:** I will review arguments that support existence of a quantum phase of matter (a condensate of charged bosons) under conditions, found in dwarf stars. The precise properties of this phase and of its long-distance fluctuations can be explored with the help of an appropriate effective field theory. After formulating the latter theory, I will briefly discuss its implications for the cooling history of Helium white dwarf stars.

11:00am **SCGP:** Quantum Mechanical Systems Program Seminar: Anton de la Fuente

**Where:** 313**When:** Fri, Sep 20 11:00am — 12:00pm

11:00am RTG Student Seminar: Jin-Cheng Guu - Coherent Sheaves

**Where:** Math Tower 5-127**When:** Fri, Sep 20 11:00am — 12:00pm

**Title:** Coherent Sheaves

**Speaker:** Jin-Cheng Guu [Stony Brook University]

**Abstract:** We will explain what coherent sheaves are, some of their cohomological properties, and sketch a proof for a reconstructing theorem: good schemes are determined by their derived category of coherent sheaves.

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1:00pm Grad / Postdoc Professional Development Seminar: Erica Klarreich - On working as a math journalist

**Where:** P-131**When:** Fri, Sep 20 1:00pm — 2:00pm

**Title:** On working as a math journalist

**Speaker:** Erica Klarreich [Freelance journalist]

**Abstract:** Erica Klarreich is a freelance journalist based in Berkeley, California. She has written for many publications, including Nature, Quanta Magazine, ScientificAmerican.com, New Scientist, American Scientist, Wired.com, Nautilus, and Science News. She is a graduate of the science writing program at the University of California, Santa Cruz, and has a Ph.D. in mathematics from Stony Brook University.

Erica's abstract: "I'll talk a bit about how I became a math journalist and what I do on a day-to-day basis, but mainly I'd like to answer people's questions." She will join us by video conference from Berkeley.

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Erica's abstract: "I'll talk a bit about how I became a math journalist and what I do on a day-to-day basis, but mainly I'd like to answer people's questions." She will join us by video conference from Berkeley.

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1:30pm **SCGP:** Physics Seminar: Amit Sever

**When:** Fri, Sep 20 1:30pm — 2:30pm

**Title:** The Holographic Dual of Strongly γ-deformed N=4 SYM Theory

**Abstract:** We present a first-principles derivation of a weak-strong duality between the four-dimensional fishnet theory in the planar limit and a discretized string-like model living in AdS5. At strong coupling, the dual description becomes classical and we demonstrate explicitly the classical integrability of the model. We test our results by reproducing the strong coupling limit of the 4-point correlator computed before non-perturbatively from the conformal partial wave expansion. Next, by applying the canonical quantization procedure with constraints, we show that the model describes a quantum integrable chain of particles propagating in AdS5. Finally, we reveal a discrete reparametrization symmetry of the model and reproduce the spectrum when known analytically. Due to the simplicity of our model, it could provide an ideal playground for holography. Furthermore, since the fishnet model and N=4 SYM theory are continuously linked our consideration could shed light on the derivation of AdS/CFT for the latter. This talk is based on recent work with Nikolay Gromov.

2:30pm Dynamical Systems Seminar: Alena Erchenko - Flexibility of Lyapunov exponents with respect to two classes of measures on the torus

**Where:** Math Tower P-131**When:** Fri, Sep 20 2:30pm — 3:30pm

**Title:** Flexibility of Lyapunov exponents with respect to two classes of measures on the torus

**Speaker:** Alena Erchenko [Stony Brook University]

**Abstract:** We consider a family of Anosov area-preserving diffeomorphisms on the two-torus that are homotopic to a fixed Anosov automorphism. There are several interesting classes of invariant measures. We will concentrate on the invariant measure that is absolutely continuous with respect to the Lebesgue measure and the measure of maximal entropy. We show that positive Lyapunov exponents with respect to these two probability measures in the considered family of diffeomorphisms take on all values that satisfy some well-known inequalities.

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4:00pm Geometric Analysis Learning Seminar: Yu Li - Colding's volume convergence theorem

**Where:** P-131 Math Tower**When:** Fri, Sep 20 4:00pm — 6:00pm

**Title:** Colding's volume convergence theorem

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

**Abstract:** Colding's theorem on volume convergence is the cornerstone for the Cheeger-Colding theory. In this talk, I will discuss the proof of the theorem that the volume is a continuous function on the space of closed manifolds with uniform Ricci lower bound in Gromov-Hausdorff topology.

Reference: Tobias H. Colding, Ricci curvature and volume convergence

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Reference: Tobias H. Colding, Ricci curvature and volume convergence

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1:00pm Student Differential Geometry Seminar: Miao Song - The Laplacian on hyperbolic space

**Where:** 5-127**When:** Mon, Sep 23 1:00pm — 2:30pm

**Title:** The Laplacian on hyperbolic space

**Speaker:** Miao Song [Stony Brook University]

**Abstract:** TBA

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12:30pm **YITP:** Anastasiia Filimonova (Heidelberg) -- "Long live the Higgs portal!"

**Where:** Math building 6125**When:** Tue, Sep 24 12:30pm — 1:30pm

Long live the Higgs portal!

~

In Higgs portal models of fermion dark matter, scalar couplings are unavoidably suppressed by strong bounds from direct detection experiments. As a consequence, thermal dark matter relics must coexist with mediators in a compressed spectrum of dark particles. Small couplings and small mass splittings lead to slow mediator decays, leaving signatures with displaced vertices or disappearing tracks at colliders.

We perform a comprehensive analysis of long-lived mediators at the LHC in the context of a

minimal dark matter model with a naturally small Higgs portal, also known as the wino-bino scenario in supersymmetry. Existing searches for disappearing charged tracks and displaced hard leptons already exclude tiny portal couplings that cannot be probed by current direct and indirect detection experiments. For larger portal couplings, we predict new signatures with displaced soft leptons, which are accessible with run-II data. Searches for displaced particles are sensitive to weakly coupling mediators with masses up to the TeV scale, well beyond the reach of prompt signals.

Long live the Higgs portal!

~

In Higgs portal models of fermion dark matter, scalar couplings are unavoidably suppressed by strong bounds from direct detection experiments. As a consequence, thermal dark matter relics must coexist with mediators in a compressed spectrum of dark particles. Small couplings and small mass splittings lead to slow mediator decays, leaving signatures with displaced vertices or disappearing tracks at colliders.

We perform a comprehensive analysis of long-lived mediators at the LHC in the context of a

minimal dark matter model with a naturally small Higgs portal, also known as the wino-bino scenario in supersymmetry. Existing searches for disappearing charged tracks and displaced hard leptons already exclude tiny portal couplings that cannot be probed by current direct and indirect detection experiments. For larger portal couplings, we predict new signatures with displaced soft leptons, which are accessible with run-II data. Searches for displaced particles are sensitive to weakly coupling mediators with masses up to the TeV scale, well beyond the reach of prompt signals.

1:00pm **SCGP:** SCGP Weekly Talk: Uri Kol

**Where:** 102**When:** Tue, Sep 24 1:00pm — 2:00pm

**Title:** Infrared structure of general relativity

1:00pm Graduate Student Seminar: Myeongjae Lee - Nonplanarity of K3,3 and the Jordan Curve Theorem

**Where:** Math Tower P-131**When:** Wed, Sep 25 1:00pm — 2:00pm

**Title:** Nonplanarity of K3,3 and the Jordan Curve Theorem

**Speaker:** Myeongjae Lee [Stony Brook University]

**Abstract:** TBA

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2:00pm **SCGP:** Physics Seminar: Uri Kol

**Where:** 313**When:** Wed, Sep 25 2:00pm — 3:00pm

4:00pm Algebraic geometry seminar: Enrica Mazzon - TBA

**Where:** Math Tower P-131**When:** Wed, Sep 25 4:00pm — 5:30pm

**Title:** TBA

**Speaker:** Enrica Mazzon [Imperial College London]

**Abstract:** TBA

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11:00am Symplectic Geometry Seminar: Kyle Hayden - Background: Knot traces, cork twists, and Floer homology

**Where:** Math Tower 5-127**When:** Thu, Sep 26 11:00am — 12:00pm

**Title:** Background: Knot traces, cork twists, and Floer homology

**Speaker:** Kyle Hayden [Columbia University]

**Abstract:** A knot trace is a 4-manifold obtained by attaching a single 2-handle to the 4-ball along a knot in its boundary. These simple 4-manifolds arise naturally in many contexts, from the construction of exotic smooth structures on R^4 and small compact 4-manifolds to the recent proof that the Conway knot is not slice. After sketching these applications, we'll talk about the role knot traces play in Floer homology.

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1:00pm Symplectic Geometry Seminar: Kyle Hayden - Exotic Mazur manifolds and knot trace invariants

**Where:** Math Tower 5-127**When:** Thu, Sep 26 1:00pm — 2:00pm

**Title:** Exotic Mazur manifolds and knot trace invariants

**Speaker:** Kyle Hayden [Columbia University]

**Abstract:** From a handlebody-theoretic perspective, the simplest compact, contractible 4-manifolds, other than the 4-ball, are Mazur manifolds. We produce the first pairs of Mazur manifolds that are homeomorphic but not diffeomorphic. Our diffeomorphism obstruction comes from the knot Floer homology concordance invariant nu, which we prove is an invariant of a simple 4-manifold associated to a knot, called the knot trace. In contrast, we also show that the concordance invariants tau and epsilon are not invariants of such 4-manifolds. As a corollary to the existence of exotic Mazur manifolds, we produce integer homology 3-spheres admitting two distinct S1xS2 surgeries, resolving a question from Problem 1.16 in Kirby's list. This is joint work with Tom Mark and Lisa Piccirillo.

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2:30pm Analysis Seminar: Mihalis Mourgoglou - PDE-characterization of uniform rectifiability and the solvability of the $L^p$-Dirichlet problem.

**Where:** P-131**When:** Thu, Sep 26 2:30pm — 3:30pm

**Title:** PDE-characterization of uniform rectifiability and the solvability of the $L^p$-Dirichlet problem.

**Speaker:** Mihalis Mourgoglou [UPV/EHU]

**Abstract:** In this talk we will discuss the connection between uniform rectifiability of the boundary of a domain with scale invariant PDE estimates for bounded harmonic functions as well as the geometric characterization of the solvability of the $L^p$-Dirichlet problem for the Laplace equation

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