For more information please visit: http://scgp.stonybrook.edu/archives/21023

10:30am **SCGP:** Fluid Dynamics Program Seminar: Takeshi Matsumoto (Department of Physics, Kyoto University)

**Where:** SCGP 313**When:** Tue, Oct 24 10:30am — 12:30pm

**Title:** Toward numerical implementation of the construction of dissipative Euler solutions with the Mikado flow

**Abstract:** Buckmaster, De Lellis, Szekelyhidi and Vicol updated recently a mathematical construction of weak solutions of the Euler equation with a prescribed energy as a function of time (arXiv:1701.08678). Moreover as well as the energy we can control the Holder exponent of the solution, which can be arbitrary close to 1/3. In the construction, so-called Mikado flow (a set of slender jets) plays an important role. We see a great potential of the solutions for a test tube of turbulence problem. Some of the quantities of interest are not easy to evaluate mathematically. Hence its numerical implementation of their method is needed. We present our ongoing work on translating their mathematical construction into a numerical simulation.

2:00pm **SCGP:** SCGP Weekly Talk: Tobias Colding

**Where:** SCGP 102**When:** Tue, Oct 24 2:00pm — 3:00pm

**Title:** Optimal regularity for geometric flows

**Abstract:** Many physical phenomema lead to tracking moving fronts whose speed depends on the curvature. The level set method has been tremendously succesful for this, but the solutions are typically only continuous. We will discuss results that show that the level set flow has twice differentiable solutions. This is optimal.

These analytical questions crucially rely on understanding the underlying geometry. Further developing these geometric techniques gives solutions to other analytical questions like Arnold-Thom conjectures for degenerate equations.

Finally, the techniques should have applications to other geometric flows. If time permits, then we will discuss results about this.

Hashtag: #workshop

These analytical questions crucially rely on understanding the underlying geometry. Further developing these geometric techniques gives solutions to other analytical questions like Arnold-Thom conjectures for degenerate equations.

Finally, the techniques should have applications to other geometric flows. If time permits, then we will discuss results about this.

Hashtag: #workshop

4:00pm Geometry/Topology Seminar: Mark Haskins - Codimension One Collapse and Special Holonomy Metrics

**Where:** SCGP 102**When:** Tue, Oct 24 4:00pm — 5:30pm

**Title:** Codimension One Collapse and Special Holonomy Metrics

**Speaker:** Mark Haskins [University of Bath]

**Abstract:** In this talk we describe recent developments related to codimension one collapse of exceptional holonomy metrics. i.e. where a family of special holonomy metrics on a space of dimension n converges in some limit to a metric on a space of dimension n-1. Interesting examples occur for hyperkaehler 4-manifolds, G_2 holonomy manifolds and Spin_7 holonomy manifolds. The talk will focus on the G_2 holonomy case, but will also draw on the better understood hyperkaehler case for inspiration and for useful analogies. These mathematical developments are closely related to important limits in physics, e.g. in the context of G_2 holonomy metrics it is related to the identification of the weak coupling limit of M theory compactified on a G_2 holonomy space being Type IIA String Theory on a 6-dimensional space. This is work joint with Lorenzo Foscolo and Johannes Nordstrom.

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5:25pm First and Second Year Student Seminar: Panel discussion - Prepare qual/comps

**Where:** Math Tower 5-127**When:** Tue, Oct 24 5:25pm — 6:30pm

**Title:** Prepare qual/comps

**Speaker:** Panel discussion [Stony Brook University]

**Abstract:** We will hold a discussion session with Ben Wu, Tobias Shin, Liz Hernandez Vazquez, and Aleksandar Milivojevic about preparing/taking qual/comps.

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1:00pm Graduate Student Seminar: Yoon-Joo Kim - Arithmetic and geometry of Dedekind domains

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

**Title:** Arithmetic and geometry of Dedekind domains

**Speaker:** Yoon-Joo Kim [Stony Brook University]

**Abstract:** Dedekind domain was originally defined in the late 19th century to solve Fermats last theorem. Although the attempt was not successful, it turned out Dedekind domains naturally arise in the study of algebraic numbers and Riemann surfaces. This explains a surprising amount of similarities between the two theories. In this talk, we will use the intuition from geometry of Riemann surfaces to understand the analogous results in classical number theory.

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1:30pm **SCGP:** Physics Seminar: Jerome Gauntlett

**Where:** SCGP 313**When:** Wed, Oct 25 1:30pm — 2:30pm

**Title:** Holographic Transport and Black Hole Horizons

**Abstract:** In seeking possible applications of holography to real materials the transport of heat and charge are basic physical

observables to analyse. Like the entropy and conserved charges we explain how the DC thermoelectric conductivity

can be obtained from the behaviour of black hole spacetimes purely at the horizon. More precisely, the DC

conductivity can be obtained by solving a generalised set of Navier-Stokes

equations for an auxiliary fluid living on the black hole horizon. Unlike other connections

between fluids and black holes, this is an exact result and and can be viewed as a precise manifestation

of the old membrane paradigm for black holes in holography. We also derive

the dispersion relations for quasi-normal hydrodynamic modes associated with diffusion of heat and charge,

obtaining a generalised Einstein relation from Einstein equations.

observables to analyse. Like the entropy and conserved charges we explain how the DC thermoelectric conductivity

can be obtained from the behaviour of black hole spacetimes purely at the horizon. More precisely, the DC

conductivity can be obtained by solving a generalised set of Navier-Stokes

equations for an auxiliary fluid living on the black hole horizon. Unlike other connections

between fluids and black holes, this is an exact result and and can be viewed as a precise manifestation

of the old membrane paradigm for black holes in holography. We also derive

the dispersion relations for quasi-normal hydrodynamic modes associated with diffusion of heat and charge,

obtaining a generalised Einstein relation from Einstein equations.

2:30pm **YITP:** CANCELLED: Joint BNL-YITP seminar @ YITP

**When:** Wed, Oct 25 2:30pm — 3:30pm

4:00pm Analysis Student Seminar: Edward Bryden - Second Variation Formula, Morse Index, and Stability

**Where:** Math Tower 5-127**When:** Wed, Oct 25 4:00pm — 5:00pm

**Title:** Second Variation Formula, Morse Index, and Stability

**Speaker:** Edward Bryden [Stony Brook University]

**Abstract:** Having developed the second variation formula last week, we continue our discussion by introducing stability and the Morse index.

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4:00pm Algebraic geometry seminar: Sebastian Casalaina-Martin - Algebraic representatives and intermediate Jacobians over perfect fields

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

**Title:** Algebraic representatives and intermediate Jacobians over perfect fields

**Speaker:** Sebastian Casalaina-Martin [U. of Colorado,. Boulder]

**Abstract:** Intermediate Jacobians and Abel--Jacobi maps provide a powerful tool for the study of complex projective manifolds. In positive characteristic, over algebraically closed fields, algebraic representatives and regular homomorphisms provide a replacement for the intermediate Jacobian and Abel--Jacobi map. I will discuss recent progress, with Jeff Achter and Charles Vial, extending this theory to the case of perfect fields, as well as some applications to a question of Barry Mazur on weight one Galois representations arising from geometry.

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2:30pm **YITP:** Theory seminar: Stefano Negro (YITP) "Non-Wilsonian RG flows and the TTbar perturbation of 2D QFT"

**Where:** YITP common room**When:** Thu, Oct 26 2:30pm — 3:30pm

**Abstract:** Since many year it is known that the confining flux tube between a quark and an anti-quark in D dimensions can be very efficiently described by the Conformal Field Theory of D-2 massless free bosons. The deviation from this theory are then well approximated by Nambu-Goto string action. Recently it was observed that these deviation can be realized, in the S-matrix framework, as the deformation of the free boson scattering matrix by a CDD factor. After a brief review of the effective string theory for confining quark-anti-quark flux tube, I will show how the presence of a non-trivial CDD factor can be interpreted as a deformation of the CFT action by an irrelevant operator constructed from the energy-momentum tensor components. This deformation enjoys peculiar properties and allows for an exact determination of the spectrum which involves an hydrodynamic-type equation. I will present the properties of this deformation and show how it can be extended to a generic, not necessarily integrable, QFT.

4:00pm Colloquium: Peter Kronheimer - Simon Donaldson's Mathematics: A Retrospective

**Where:** SCGP 102**When:** Thu, Oct 26 4:00pm — 5:30pm

**Title:** Simon Donaldson's Mathematics: A Retrospective

**Speaker:** Peter Kronheimer [Harvard University]

**Abstract:** This talk will provide a personal perspective on some of Simon Donaldson's

many important contributions to the geometry and topology of manifolds.

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many important contributions to the geometry and topology of manifolds.

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2:30pm Dynamical Systems Seminar: Babak Modami - Renormalization in Teichmuller dynamics

**Where:** Math Tower P-131**When:** Fri, Oct 27 2:30pm — 3:30pm

**Title:** Renormalization in Teichmuller dynamics

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

**Abstract:** After a brief review of Masur's criterion which is an example of the renormalization technique in Teichmuller dynamics, we show that an analogue of the criterion does not hold for the Weil-Petersson geodesic flow. The talk is based on a joint work with Jeff Brock from 2015.

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1:00pm RTG Seminar: Yoonjoo Kim - Degenerations of Hodge Structures

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

**Title:** Degenerations of Hodge Structures

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

**Abstract:** TBA

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4:00pm Special Algebra / Algebraic Geometry Seminar: Remy van Dobben de Bruyn - Dominating varieties by liftable ones.

**Where:** Math Tower P-131**When:** Mon, Oct 30 4:00pm — 5:30pm

**Title:** Dominating varieties by liftable ones.

**Speaker:** Remy van Dobben de Bruyn [Columbia University]

**Abstract:** Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

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Halloween

**When:** Tue, Oct 31

1:00pm **SCGP:** SCGP Weekly Talk: Olaf Hohm

**Where:** SCGP 102**When:** Tue, Oct 31 1:00pm — 2:00pm

**Title:** L-infinity algebra and field theory

4:00pm Geometry/Topology Seminar: Nishanth Gudapati - TBA

**Where:** Math Tower P-131**When:** Tue, Oct 31 4:00pm — 5:30pm

**Title:** TBA

**Speaker:** Nishanth Gudapati [Yale University]

**Abstract:**

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1:00pm Graduate Student Seminar: Chase Middleman - TBA

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

**Title:** TBA

**Speaker:** Chase Middleman [Stony Brook University]

**Abstract:** TBA

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1:30pm **SCGP:** Physics Seminar: Pietro Benetti Genolini

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

**Title:**

**Abstract:**

4:00pm Analysis Student Seminar: Jack Burkart - Weierstrass Representation and The Strong Maximum Principle

**Where:** Math Tower 5-127**When:** Wed, Nov 1 4:00pm — 5:00pm

**Title:** Weierstrass Representation and The Strong Maximum Principle

**Speaker:** Jack Burkart [Stony Brook University]

**Abstract:** We'll discuss the following things:

1. The Weierstrass representation of a minimal surface.

2. The Schwarz Reflection Principle

3. The Strong Maximum Principle for minimal hypersurfaces.

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1. The Weierstrass representation of a minimal surface.

2. The Schwarz Reflection Principle

3. The Strong Maximum Principle for minimal hypersurfaces.

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4:00pm Algebraic geometry seminar: Inna Zakharevich - Constructing derived motivic measures

**Where:** Math Tower P-131**When:** Wed, Nov 1 4:00pm — 5:30pm

**Title:** Constructing derived motivic measures

**Speaker:** Inna Zakharevich [Cornell]

**Abstract:** Motivic measures can be thought of as homomorphisms out of the Grothendieck ring of varieties. Two well-known such measures are the Larsen--Lunts measure (over $\mathbf{C}$) and the Hasse--Weil zeta function (over a finite field). In this talk we will show how to lift the Hasse--Weil zeta function to a map of $K$-theory spectra which restricts to the usual zeta function on $K_0$. As an application we will show that the Grothendieck spectrum contains nontrivial elements in the higher homotopy groups.

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