Seminars and Colloquia by Series

Friday, December 1, 2017 - 14:00 , Location: Skiles 006 , Bunimovich, Fathi, Grigoriev, de la Llave and Zeng , GT Math and Physics , Organizer: Sung Ha Kang
Thursday, November 30, 2017 - 15:05 , Location: Skiles 006 , Matthew Junge , Duke University , jungem@math.duke.edu , Organizer: Gerandy Brito
Cars are placed with density p on the lattice. The remaining vertices are parking spots that can fit one car. Cars then drive around at random until finding a parking spot. We study the effect of p on the availability of parking spots and observe some intriguing behavior at criticality. Joint work with Michael Damron, Janko Gravner, Hanbeck Lyu, and David Sivakoff. arXiv id: 1710.10529.
Thursday, November 30, 2017 - 13:30 , Location: Skiles 005 , Shijie Xie , Math, Gt , Organizer: Robin Thomas
Let G be a graph containing 5 different vertices a0, a1, a2, b1 and b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and {b1, b2}⊆V(G2). In this talk, we will complete a sketch of our arguments for characterizing when (G, a0, a1, a2, b1, b2) is feasible. Joint work with Changong Li, Robin Thomas, and Xingxing Yu.
Thursday, November 30, 2017 - 11:05 , Location: Skiles 006 , Zhou Fan , Stanford University , zhoufan@stanford.edu , Organizer: Michael Damron
Random effects models are commonly used to measure genetic variance-covariance matrices of quantitative phenotypic traits. The population eigenvalues of these matrices describe the evolutionary response to selection. However, they may be difficult to estimate from limited samples when the number of traits is large. In this talk, I will present several results describing the eigenvalues of classical MANOVA estimators of these matrices, including dispersion of the bulk eigenvalue distribution, bias and aliasing of large "spike" eigenvalues, and distributional limits of eigenvalues at the spectral edges. I will then discuss a new procedure that uses these results to obtain better estimates of the large population eigenvalues when there are many traits, and a Tracy-Widom test for detecting true principal components in these models. The theoretical results extend proof techniques in random matrix theory and free probability, which I will also briefly describe.This is joint work with Iain Johnstone, Yi Sun, Mark Blows, and Emma Hine.
Wednesday, November 29, 2017 - 13:55 , Location: Skiles 005 , Catherine Beneteau , University of South Florida , Organizer: Shahaf Nitzan
    In this talk, I will discuss some polynomials that are best approximants (in some sense!) to reciprocals of functions in some analytic function spaces of the unit disk.  I will examine the extremal problem of finding a zero of minimal modulus, and will show how that extremal problem is related to the spectrum of a certain Jacobi matrix and real orthogonal polynomials on the real line.
Wednesday, November 29, 2017 - 13:55 , Location: Skiles 006 , Anubhav Mukherjee , Georgia Tech , Organizer: Jennifer Hom
I'll try to describe some known facts about 3 manifolds. And in the end I want to give some idea about Geometrization Conjecture/theorem.
Wednesday, November 29, 2017 - 12:10 , Location: Skiles 006 , Chongchun Zeng , Georgia Tech , Organizer:
In this talk, we consider the structure of a real $n \times n$ matrix in the form of $A=JL$, where $J$ is anti-symmetric and $L$ is symmetric. Such a matrix comes from a linear Hamiltonian ODE system with $J$ from the symplectic structure and the Hamiltonian energy given by the quadratic form $\frac 12\langle Lx, x\rangle$. We will discuss the distribution of the eigenvalues of $A$, the relationship between the canonical form of $A$ and the structure of the quadratic form $L$, Pontryagin invariant subspace theorem, etc. Finally, some extension to infinite dimensions will be mentioned.    
Series: PDE Seminar
Tuesday, November 28, 2017 - 15:00 , Location: Skiles 006 , Eduardo Teixeira , University of Central Florida , eduardo.teixeira@ucf.edu , Organizer: Yao Yao
Geometric tangential analysis refers to a constructive systematic approach based on the concept that a problem which enjoys greater regularity can be “tangentially" accessed by certain classes of PDEs. By means of iterative arguments, the method then imports regularity, properly corrected through the path used to access the tangential equation, to the original class. The roots of this idea likely go back to the foundation of De Giorgi’s geometric measure theory of minimal surfaces, and accordingly, it is present in the development of the contemporary theory of free boundary problems. This set of ideas also plays a decisive role in Caffarelli’s work on fully non-linear elliptic PDEs, and subsequently in his studies on Monge-Ampere equations from the 1990’s. In recent years, however, geometric tangential methods have been significantly enhanced, amplifying their range of applications and providing a more user-friendly platform for advancing these endeavors. In this talk, I will discuss some fundamental ideas supporting (modern) geometric tangential methods and will exemplify their power through select examples.
Tuesday, November 28, 2017 - 13:00 , Location: Skiles 006 , Ian Jauslin , IAS, Princeton , jauslin@ias.edu , Organizer: Federico Bonetto
In 1979, O. Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.
Tuesday, November 28, 2017 - 11:00 , Location: Skiles 006 , Vieri Mastropietro , Universita' di Milano, Italy , vieri.mastropietro@unimi.it , Organizer: Federico Bonetto
Abstract: A number of quantities in quantum many-body systems show remarkable universality properties, in the sense of exact independence from microscopic details. I will present some rigorous result establishing universality in presence of many body interaction in Graphene and in Topological Insulators, both for the bulk and edge transport. The proof uses Renormalization Group methods and a combination of lattice and emerging Ward Identities.

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