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-131When: 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]
10:00am RTG Student Geometry Seminar: Ben Wu - Higgs Bundles and Local Systems Where: Math Tower 5-127When: Fri, Apr 26 10:00am — 11:00am Title: Higgs Bundles and Local Systems Speaker: Ben Wu [Stony Brook University]
Abstract: We continue discussing Simpson's notion of a pure non-Abelian Hodge structure. We will discuss how the results from previous sections of Simpson's paper can be interpreted as the existence of a pure non-Abelian Hodge structure for compact Khler manifolds. We will then describe how this additional structure places restrictions on which groups can be the fundamental group of a compact Khler manifold. View Details
11:00am Thesis Defense: Fangyu Zou - Monge-Ampre equation on the complement of a divisor Where: Physics P-129When: 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. View Details
2:00pm Thesis Defense: Zhongshan An - Ellipticity of Bartnik Boundary Data for Stationary Vacuum Spacetimes Where: Physics P-123When: 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. View Details
2:30pm Dynamical Systems Seminar: Saeed Zakeri - On the correspondence of external rays under renormalization Where: Math Tower P-131When: 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. View Details
4:00pm Geometric Analysis Learning Seminar: Yu Li - Almost flat manifolds Where: P-131 Math TowerWhen: 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 View Details
Monday, April 29
SCGP: Convergence and Low Regularity in General Relativity When: Mon, Apr 29 — Fri, May 3 For more information please visit: http://scgp.stonybrook.edu/archives/25455
2:30pm SCGP: Weekly Physics Meeting: Zohar Komargodski Where: 313When: Mon, Apr 29 2:30pm — 3:30pm Title: Some remarks on Baryons in QCD
Abstract: In the late 70's, the question of whether tori could admit metrics of positive scalar curvature was being tackled by Gromov and Lawson (here at Stony Brook), and independently by Schoen and Yau. The former duo developed the notion of enlargeability to settle the question in the negative, while the latter developed their minimal hypersurface technique which, until very recently, limited their conclusion to dimension at most 7.
In this talk I will define enlargeability and indicate its relationship to the existence of positive scalar curvature metrics. View Details
Tuesday, April 30
1:00pm SCGP: SCGP Weekly Talk: Philippe LeFloch Where: 102When: Tue, Apr 30 1:00pm — 2:00pm Title: A geometric analysis view on spacetimes: stability and singularities
Abstract: I will overview, in a non-technical manner, some recent mathematical results on the Einstein equations of general relativity, especially on understanding nonlinear geometry-matter interactions. Are self-gravitating matter fields nonlinearly stable near Minkowski spacetime ? In what quantitative sense does the curvature provide a control of the spacetime geometry ? What happens when two plane gravitational waves collide ? Blog: philippelefloch.org
1:00pm Grad / Postdoc Professional Development Seminar: Graduate students - Jobs after graduation II Where: P-131When: Tue, Apr 30 1:00pm — 2:00pm Title: Jobs after graduation II Speaker: Graduate students [Stony Brook University]
Abstract: Some of our graduate students who are finishing this year are going to share their experience in looking for jobs. Today: Michael Albanese (Postdoc at Universit du Qubec Montral), Aleksander Doan (Postdoc at Columbia University), and Fangyu Zou (Applied Machine Learning Developer at Facebook). View Details
2:00pm YITP: Anna Hasenfratz (U. Colorado)--"Hidden Properties of Composite Systems in and out of the Conformal Window" (note special day and time) Where: YITP Common RoomWhen: Tue, Apr 30 2:00pm — 3:00pm Abstract Lattice QCD methods allow the study of non-perturbative properties of strongly coupled systems. The QCD spectrum, including excited states, or hadronic matrix elements, have been calculated with high precision. Investigations of conformal or near-conformal systems that might describe beyond-Standard Model phenomenology are less advanced, but interesting observations are emerging from lattice studies. While QCD and conformal systems might appear rather different, their renormalization group structures have a lot in common. A recently introduced method that allows the calculation of the anomalous dimensions of composite fermionic operators is, in fact, applicable to both. In this talk I will discuss this method that combines real-space renormalization group transformation with gradient flow, and briefly show some new results both in QCD and conformal models.
(host: Robert Shrock)
4:15pm SCGP: Physics Colloquium: Ulf Meissner Where: Harriman 137When: Tue, Apr 30 4:15pm — 5:15pm Coffee and Tea at 3:45 Full Schedule: http://www.physics.sunysb.edu/Physics/colloquium/2018/
Wednesday, May 1
1:00pm SCGP: Hitchin Systems Program Seminar: Nigel Hitchin Where: SCGP 313When: Wed, May 1 1:00pm — 2:30pm Title: Subintegrable systems and their special Kahler metrics
Abstract: The critical loci of the Higgs bundle moduli space define subintegable systems. As such they admit a natural semiflat hyperkahler metric determined by the special Kahler metric on the base. We shall consider the Kahler potential in terms of the singular spectral curve.
2:30pm YITP: Joint BNL-SBU pheno seminar @ BNL: James Wells Where: BNLWhen: Wed, May 1 2:30pm — 3:30pm
2:30pm YITP: Andrea Trombettoni (CNR & SISSA, Trieste, Italy) & Nicolo' Defenu (Heidelberg University, Germany)--"Equilibrium and Dynamical Properties of Quantum Long-Range Spin Systems" Where: YITP Common RoomWhen: Wed, May 1 2:30pm — 3:30pm
Title: Equilibrium and Dynamical Properties of Quantum Long-Range Spin Systems
Several recent experiments in atomic, molecular and optical systems motivated a huge interest in the study of quantum long-range spin systems. In the first part of the talk [by Andrea Trombettoni] we discuss a general description of their critical behavior and phases, devising a treatment valid in d dimensions, with an exponent d+\sigma for the power-law decay of the couplings in the presence of an O(N) symmetry. Results for the correlation length exponent, the dynamical critical exponent z and a comparison with numerical findings for them are presented. In the second part of the talk [30minutes, by Nicolo' Defenu], the goal is to present a discussion of dynamical properties of quantum long-range systems, focusing on slow quenches. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. Slow quenches of the magnetic field in quantum long-range quantum systems are then analyzed, showing that it is possible to analytically determine the quantum contribution to the residual heat as a function of the quench rate by means of a Holstein-Primakoff expansion about the mean-field value.
(host: Vladimir Korepin)
4:00pm Analysis Student Seminar: Paul Sweeney - Multiple valued functions minimizing the Dirichlet energy Where: Math Tower 5-127When: Wed, May 1 4:00pm — 5:00pm Title: Multiple valued functions minimizing the Dirichlet energy Speaker: Paul Sweeney [Stony Brook University]
Abstract: We discusse yet another important tool in the regularity theory, Q-valued maps and Dir-minimizers. (This is our last seminar for the semester) View Details
4:00pm Algebraic geometry seminar: Andrew Obus - Fun with Mac Lane valuations Where: Math Tower P-131When: Wed, May 1 4:00pm — 5:30pm Title: Fun with Mac Lane valuations Speaker: Andrew Obus [Baruch College CUNY]
Abstract: Mac Lane's technique of "inductive valuations" is over 80 years old, but has only recently been used to attack problems about arithmetic surfaces. We will give an explicit, hands-on introduction to the theory, requiring little background beyond the definition of a valuation on a ring. We will then outline how this theory is helpful for resolving "weak wild" quotient singularities of arithmetic surfaces, as well as for proving conductor-discriminant inequalities for higher genus curves. The first project is joint with Stefan Wewers, and the second is joint work with Padmavathi Srinivasan. View Details
2:30pm Dynamical Systems Seminar: Sabya Mukherjee - Dynamics of Schwarz reflections: Mating rational maps with groups Where: Math Tower P-131When: Fri, May 3 2:30pm — 3:30pm Title: Dynamics of Schwarz reflections: Mating rational maps with groups Speaker: Sabya Mukherjee [Stony Brook University]
Abstract: Quadrature domains are planar domains admitting a global Schwarz reflection map. As dynamical systems, Schwarz reflection maps produce various instances of matings of rational maps and groups.
In this talk, we will focus on a one-parameter family of Schwarz reflection maps. Using a straightening theorem for ``pinched quadratic-like maps", we will show that each map in this family is hybrid equivalent to a quadratic anti-holomorphic rational map. We will also describe how such maps lead to anti-holomorphic correspondences that are matings of anti-holomorphic rational maps and the abstract modular group.
Joint work with Seung-Yeop Lee, Mikhail Lyubich, and Nikolai Makarov. View Details