1:00pm SCGP: SCGP Weekly Talk: Michael Anderson When: Tue, Oct 16 1:00pm — 2:00pm Title: Boundaries in Euclidean and Lorentzian Gravity
Abstract: There is no existence theory for Riemannian Einstein metrics on compact manifolds, while there is an excellent theory for Lorentzian Einstein metrics (GR). What happens when one puts in a boundary, creating a boundary value problem - at finite or infinite distance? What are the correct boundary data? This makes the Riemannian existence problem more amenable - one can start to build a theory, but the Lorentzian problem becomes more difficult. The talk will discuss some results, perspectives and open problems in this area.
4:15pm SCGP: Physics Colloquium: Alexios Polychronakos Where: Harriman 137 When: Tue, Oct 16 4:15pm — 5:15pm Coffee and Tea at 3:45 Full Schedule: http://www.physics.sunysb.edu/Physics/colloquium/2018/
5:30pm First and Second Year Student Seminar: Dennis Sullivan - The idea of manifolds with singularities Where: Math Tower 5-127When: Tue, Oct 16 5:30pm — 6:30pm Title: The idea of manifolds with singularities Speaker: Dennis Sullivan [Stony Brook University]
Abstract: These include algebraic varieties over C or R, analytic varieties over R or C and significantly the cycles and homologies in the so-called singular homology. Complex varieties give integral cycles of even dimension, while real varieties give mod two cycles. The singular definition of usual homology can be pictured by constructing a geometric realization of a singular chain, gluing the pieces together. To "compute" all of these things requires a general pictorial scheme which was provided by Thom and Whitney. View Details
Wednesday, October 17
1:00pm Graduate Student Seminar: Jin-Cheng Guu - A Generalization of Fourier Analysis Where: Math Tower P-131When: Wed, Oct 17 1:00pm — 2:00pm Title: A Generalization of Fourier Analysis Speaker: Jin-Cheng Guu [Stony Brook University]
Abstract: Lets see how a group G (compact, connected) smoothly acts on a complex vector space. A fundamental case is when G is abelian (Fourier series), whose applications can be found in PDE, ergodic problems, number theory,... etc. We will then look at the easiest nonabelian case and a basic application to Quantum Mechanics if time permits. This talk is an invitation to an upcoming mini-seminar on representations of compact Lie groups.
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1:30pm SCGP: Physics Seminar: Avner Karasik Where: SCGP 313When: Wed, Oct 17 1:30pm — 2:30pm Title: On the phase diagram of SU(N)XSU(N) gauge theory with bifundamental Fermion.
Abstract: We study the phase diagram of SU(N)XSU(N) gauge theory with massive bifundamental Fermion at zero temperature. Assuming that the theory is con fining and gapped, some constraints that come from anomalies can be put on the phase diagram as a function of the two theta- angles. We combine these constraints with computations that are valid in the large mass and small mass limits to construct the phase diagram also for intermediate mass.
2:30pm Mini Course / Dynamics Learning Seminar: Nguyen-Bac Dang - Degree growth of tame automorphisms (part II) Where: Math Tower P-131When: Wed, Oct 17 2:30pm — 3:30pm Title: Degree growth of tame automorphisms (part II) Speaker: Nguyen-Bac Dang [Stony Brook University]
Abstract: In the first part, I explained the construction of the square complex due to Bisi-Furter-Lamy and explained the growth of the degree for the elements whose action on it fixed a vertex. In the second part of this mini course, I will focus on the automorphisms whose action on the complex is hyperbolic. First I will present the valuative estimates derived from the work of Shestakov-Umirbaev which will allow me to relate the degree with the distance in the square complex introduced by Bisi-Furter-Lamy.
Then I will present the main steps of my proof through an explicit example. View Details
4:00pm Algebraic geometry seminar: Matt Kerr - Hodge theory of degenerations Where: Math Tower P-131When: Wed, Oct 17 4:00pm — 5:30pm Title: Hodge theory of degenerations Speaker: Matt Kerr [Washington University in St Louis]
Abstract: The asymptotics and monodromy of periods in degenerating families of algebraic varieties are encountered in many settings -- for example, in comparing (GIT, KSBA, Hodge-theoretic) compactifications of moduli, in computing limits of geometric normal functions, and in topological string theory. In this talk, based on work with Radu Laza, we shall describe several tools (beginning with classical ones) for comparing the Hodge theory of singular fibers to that of their nearby fibers, and touch on some relations to birational geometry. View Details
2:30pm Analysis Seminar: Matthew Badger - Traveling along Hlder curves Where: P-131When: Thu, Oct 18 2:30pm — 3:30pm Title: Traveling along Hlder curves Speaker: Matthew Badger [University of Connecticut]
Abstract: One goal of geometric measure theory is to understand a measure through its interaction with canonical lower dimension sets. The interaction of Radon measures in the plane or a higher-dimensional Euclidean space with finite sets or rectifiable curves is now completely understood. However, with respect to any other elementary family of sets, we only know how measures behave under additional regularity hypotheses. To make progress towards understanding the structure of Radon measures, we need to first understand the geometry of more classes of sets.
I will describe my latest work with L. Naples and V. Vellis, in which we find sufficient conditions to identify (subsets of) Hlder continuous curves of Hausdorff dimension $s>1$. Our conditions are related to the Analyst's Traveling Salesman Theorem, which characterizes subsets of rectifiable curves. On the other hand, standard self-similar sets such as the Sierpinski carpet show that our sufficient condition is not necessary. I will discuss this and other obstructions to the problem of characterizing Hlder curves and their subsets. View Details
4:00pm Colloquium: Ailana Fraser - Geometries that optimize eigenvalues Where: Math Tower P-131When: Thu, Oct 18 4:00pm — 5:00pm Title: Geometries that optimize eigenvalues Speaker: Ailana Fraser [UBC]
Abstract: When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases it makes sense to attempt to find critical points in the space of metrics. For surfaces, the critical metrics turn out to be the induced metrics on certain special classes of minimal (mean curvature zero) surfaces in spheres and Euclidean balls. The eigenvalue extremal problem is thus related to other questions arising in the theory of minimal surfaces. In this talk we will give an overview of progress that has been made for surfaces with boundary, and contrast this with some recent results in higher dimensions. This is joint work with R. Schoen. View Details
Friday, October 19
11:00am SCGP: Exactly Solvable Program Seminar: Jacopo Viti Where: 313When: Fri, Oct 19 11:00am — 12:00pm Title: Exact logarithmic boundary connectivities in 2d critical percolation
Abstract: I will conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional Q-color Potts model. I in particular will provide results for the limit Q->1 that corresponds to percolation, a non-unitary CFT where the observable has a logarithmic singularity. These conjectures are tested against Monte Carlo simulations showing excellent agreement for Q=1,2 and 3.
4:00pm Geometric Analysis Learning Seminar: Vardan Oganesyan - Differential geometry and algebraic geometry Where: P-131 Math TowerWhen: Fri, Oct 19 4:00pm — 6:00pm Title: Differential geometry and algebraic geometry Speaker: Vardan Oganesyan [Stony Brook University]
Abstract: In this talk, we are going to construct minimal Lagrangian submanifolds without any knowledge in differential geometry. We will consider applications of algebraic geometry in differential and symplectic geometry. As an example, we will describe all minimal Lagrangian tori immersed in CP^2 and construct some minimal submanifolds immersed in CP^n. View Details
Monday, October 22
SCGP: Super martin: Geometrical Aspects of Supersymmetry When: Mon, Oct 22 — Fri, Oct 26 For more information please visit: http://scgp.stonybrook.edu/archives/24606
11:30am SCGP: Exactly Solvable Program Seminar: Helen Au-Yang Perk Where: 313When: Mon, Oct 22 11:30am — 12:30pm Title: Ising Models with Holes: Crossover and Proximity Effects
Abstract: To gain more theoretical insight into proximity effects studied experimentally by Gasparini et al., we study here the specific heats of special planar Ising models, which consist of periodically repeated strips of width $m$ lattice spacings and in which the coupling energy between the nearest-neighbor Ising spins is $J$. The strips are connected one to another by sequences of strings of length $n$ on which the pair interaction is also $J$. These strings are separated from one another by a distance $N$. We have studied the specific heat of these models using the dimer method. We find that the critical temperature $T_c(N,m,n)$, arising from the collective effects, decreases as $n$ and $N$ increase, and increases as $m$ increases, as it should be. The amplitude $A(N,m,n)$ of the logarithmic divergence at the bulk critical temperature $T_c(N,m,n)$ becomes smaller as $n$ and $m$ increase. A rounded peak, with size of order $\ln m$ and signifying the one-dimensional behavior of strips of finite width $m$, appears when $n$ is large enough. The appearance of these rounded peaks does not depend on $m$ as much, but depends rather more on $N$ and $n$, which is rather perplexing. Moreover, for fixed $m$ and $n$, the specific heats are not much different for different $N$. This is an other surprising result. For $N = 1$, the spin-spin correlation in the center row of each strip can be written as a Toeplitz determinant with a generating function which is much more complicated than in Onsager's Ising model. The spontaneous magnetization in that row can be calculated numerically and the spin-spin correlation is shown to have two-dimensional Ising behavior.
4:00pm Geometry/Topology Seminar: Xujia Chen - Kontsevich-type recursions for counts of real curves Where: Math Tower P-131When: Tue, Oct 23 4:00pm — 5:30pm Title: Kontsevich-type recursions for counts of real curves Speaker: Xujia Chen [Stony Brook University]
Abstract: Kontsevich's recursion, proved by Ruan-Tian in the early 90s, enumerates rational curves in complex surfaces. Welschinger defined invariant signed counts of real rational curves in real surfaces (complex surfaces with a conjugation) in 2003. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline for adapting Ruan-Tian's homotopy style argument to the real setting. For many symplectic fourfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves. View Details
4:15pm SCGP: Physics Colloquium: Robert Austin Where: Harriman 137 When: Tue, Oct 23 4:15pm — 5:15pm Coffee and Tea at 3:45 Full Schedule: http://www.physics.sunysb.edu/Physics/colloquium/2018/
Wednesday, October 24
4:00pm Algebraic geometry seminar: Will Sawin - What circles can do for you Where: Math Tower P-131When: Wed, Oct 24 4:00pm — 5:30pm Title: What circles can do for you Speaker: Will Sawin [Columbia University]
Abstract: In joint work with Tim Browning, we study the moduli spaces of rational curves on smooth hypersurfaces of very low degree (say, a degree $d$ hypersurface in $n$ variables in $n > 3 (d-1)2^{d-1}$). We show these moduli spaces are integral locally complete intersections and that they are smooth outside a set of high codimension. We get stronger results, with better codimensions, as the degrees of the rational curves grow. These results rely on the circle method from analytic number theory. I will explain how this application works, and how the same technique should apply to recent conjectures of Peyre about rational points on these hypersurfaces. View Details
5:30pm SCGP: Special Colloquium: Ulf Lindstrom, "Martin Rocek in and out of Superspace" Where: SCGP 102When: Wed, Oct 24 5:30pm — 6:30pm Colloquium Title: Martin Rocek in and out of Superspace.