Mathematics Colloquium

Organizers: Patrick Brosnan and Sandra Cerrai
When: Wednesday @ 3:15pm, 2:45pm Tea in 3201
Where: Math 3206
From time to time special colloquia are held on other days, sometimes as part of conferences.
Other special colloquia are the Aziz Lectures and Avron Douglis Memorial Lectures.

  • TBA


    Speaker: Irena Lasiecka (Universityof Memphis) - http://www.msci.memphis.edu/faculty/lasiecka.html

    When: Wed, April 30, 2014 - 3:15pm
    Where: Math 3206

  • TBA (Aziz Lecture)


    Speaker: Lenya Ryzhik (Stanford University) - http://math.stanford.edu/~ryzhik/

    When: Wed, April 23, 2014 - 3:15pm
    Where: Math 3206

  • TBA


    Speaker: Vladimir Sverak (University of Minnesota) - http://www.math.umn.edu/~sverak/

    When: Wed, April 16, 2014 - 3:15pm
    Where: Math 3206

  • Reichstein (TBA)


    Speaker: Zinovy Reichstein (University of British Columbia) - http://www.math.ubc.ca/~reichst/

    When: Wed, April 2, 2014 - 3:15pm
    Where: Math 3206

  • (February Fourier Talks)


    Speaker: Gerald Folland (University of Washington) - http://www.math.washington.edu/People/fac_individ.php?mathid=folland

    When: Fri, February 21, 2014 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: The group of operators on L2(R) generated by a single translation f(t) → f(t+1) and a single modulation f(t) → e2πiωtf(t) is a familiar object of study in signal analysis. It forms a unitary representation of the so-called discrete Heisenberg group. As such, its analysis yields easily to classical methods when ω is rational. But when ω is irrational, it provides instructive concrete examples of several pathological representation-theoretic phenomena. We shall introduce the relevant concepts from representation theory, discuss the rational case briefly, and then explore the irrational case in more detail.

  • TBA


    Speaker: Leonid Polterovich (Tel Aviv University) - https://sites.google.com/site/polterov/home

    When: Wed, February 12, 2014 - 3:15pm
    Where: Math 3206

  • TBA


    Speaker: James A. Sethian (University of California at Berkley) - http://math.berkeley.edu/people/faculty/james-sethian

    When: Wed, February 5, 2014 - 3:15pm
    Where: Math 3206

  • The Mathematics of Supersymmetry: Graphs, Codes, and Super-Curves


    Speaker: Charles Doran (University of Alberta) -

    When: Wed, December 11, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: In physics, supersymmetry is a pairing between bosons and fermions appearing in theories of subatomic particles. One may study supersymmetry mathematically by using Adinkras, which are graphs with vertices representing the particles in a supersymmetric theory and edges corresponding to the supersymmetry pairings. In combinatorial terms, Adinkras are N-regular, edge N-colored bipartite graphs with signs assigned to the edges and heights assigned to the vertices, subject to certain conditions. We will see how to capture some of the structure of an Adinkra using binary linear error-correcting codes, and all of it using a very special case of a geometric construction due to Grothendieck. The talk is designed to be accessible to an undergraduate audience.

  • The geometry of noncompact Calabi-Yau manifolds


    Speaker: Hans-Joachim Hein (Imperial College London) - http://www2.imperial.ac.uk/~hhein/

    When: Fri, December 6, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: A Calabi-Yau manifold is a complex Kahler manifold with vanishing first Chern class. This seemingly innocent topological condition has many remarkable consequences. Of particular interest is Yau's 1978 landmark theorem showing that such manifolds, if compact, admit Ricci-flat Kahler metrics - a feat of nonlinear analysis, and one of very few general sources of solutions to the Einstein equations in Riemannian geometry. A longstanding question in the field asks for extensions of Yau's theorem to noncompact settings and particularly for the possible asymptotics of noncompact Ricci-flat manifolds at infinity or at a singularity. I will survey recent progress on this question, mainly based on the point of view that a detailed understanding of the Riemannian geometry of the problem is key to proving useful estimates.

  • On symplectic isoperimetry, billiards, and Mahler's conjecture


    Speaker: Shiri Artstein ( Tel Aviv University) - http://www.tau.ac.il/~shiri/

    When: Wed, December 4, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: We shall discuss an isoperimetric conjecture regarding capacities of convex sets (called Viterbo's conjecture) and explain how it implies the well known Mahler conjecture from convexity, regarding the minimizers, among symmetric convex bodies, of the volume product of a body and its polar. The connection uses some new results on billiard dynamics, which we shall explain as well. Based of joint work with Yaron Ostrover and with Roman Karasev.

  • Extension and approximation of functions


    Speaker: Charles Fefferman (Princeton University) - https://www.math.princeton.edu/directory/charles-fefferman

    When: Tue, December 3, 2013 - 12:30pm
    Where: Math 3206

    View Abstract

    Abstract: Let X be your favorite Banach space of continuous functions on R^n. Let f be a function defined on an (arbitrary) given subset E of R^n. How can we decide whether f extends to a function F in X? If such an F exists, then how small can we take its norm? What can we say about the derivatives of F at a given point? Can we take F to depend linearly on f? What if we relax the requirement that F=f on E exactly, and just require that F-f must be small (in some sense) on E?

    Suppose E is a large finite set. Can we compute an F as above with norm close to least possible? If so, how many computer operations does it take? What if we are allowed to discard a few points of E as "outliers"? Which points should we discard?

    These questions have fascinated me for about the last ten years. In this talk I'll sketch the current state of the art.

  • What is K-theory and what is it good for?


    Speaker: Paul Baum (Penn State) - http://www.math.psu.edu/baum/

    When: Wed, November 20, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: The talk will consist of four points:

    1. The basic definition of K-theory
    2. A brief history of K-theory
    3. Algebraic versus topological K-theory
    4. The unity of K-theory

    This is an expository talk intended for a general mathematical audience.

  • Division algebras and representations of Lie groups


    Speaker: Benjamin Antieau (University of Washington) - http://www.math.washington.edu/~bantieau/

    When: Fri, November 15, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: I will give a basic introduction to principal bundles over different kinds of spaces, and I will discuss the various spaces that classify these bundles. A key insight is that even topologically these bundles can be classified by maps to complex algebraic varieties. This led Atiyah and Hirzebruch to the first counterexamples to the original, integral Hodge conjecture. I will discuss how a different approach to these algebraic classifying spaces, due to Totaro, led Ben Williams and myself to a method for answering concrete questions about division algebras over fields, and I will explain how these ideas resulted in our answer to a question in algebra from 1960.

  • Separation of variables in algebraic geometry


    Speaker: Douglas Ulmer (Georgia Tech) - http://people.math.gatech.edu/~ulmer/

    When: Wed, November 13, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Algebraic varieties (zero sets of families of multivariate polynomials) are notoriously "rigid". One manifestation of this is that a typical surface (2-dimensional variety) does not admit any surjective map from a product of two curves. I will describe a simple construction of large families of surfaces that do admit such maps, and explain some of the wonderful arithmetic consequences that follow. One nice application is to the construction of elliptic curves (and higher genus Jacobians) with large rank over function fields.

  • (AZIZ LECTURE) Universality and chaos in clustering and branching processes


    Speaker: Robert Pego (Carnegie Mellon University) - http://www.math.cmu.edu/~bobpego/

    When: Fri, November 8, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Scaling limits of Smoluchowski's coagulation equation are related to probability theory in numerous remarkable ways. E.g., such an equation governs the merging of ancestral trees in critical branching processes, as observed by Bertoin and Le Gall. A simple explanation of this relies on how Bernstein functions relate to a weak topology for Levy triples. From the same theory, we find the existence of `universal' branching mechanisms which generate complicated dynamics that contain arbitrary renormalized limits. I also plan to describe a remarkable application of Bernstein function theory to a coagulation-fragmentation model introduced in fisheries science to explain animal group size.

  • Some results for Allen-Cahn phase transition models


    Speaker: Paul Rabinowitz (University of Wisconsin) -

    When: Wed, October 30, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: We will survey some recent work on Allen-Cahn phase transition models.
    Earlier work involved the construction of solutions with transitions occurring in one spatial direction.
    For the newer models, much more general transition regions can be constructed.

  • No Colloquium


    Speaker: No Colloquium (UMD) -

    When: Wed, October 23, 2013 - 3:15pm
    Where: Math 3206

  • No Colloquium


    When: Wed, October 16, 2013 - 3:15pm
    Where: Math 3206

  • Oriented cohomology of projective homogeneous spaces


    Speaker: Kirill Zainoulline (University of Ottawa) - http://mysite.science.uottawa.ca/kzaynull/

    When: Mon, October 14, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Oriented cohomology theories and the associated formal groups laws have
    been a subject of intensive investigations since 60's, mostly inspired by
    the theory of complex cobordism. In the present talk we discuss several recent developments in the study of algebraic analogues of such theories, e.g. algebraic cobordism of Levine-Morel or algebraic elliptic cohomology, of projective homogeneous spaces.

  • A New Question on the x2,x3 Action on the 1-Torus


    Speaker: Hillel Furstenberg (Hebrew University of Jerusalem)

    When: Wed, October 9, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: For a natural number m, let f_m denote multiplication by m mod 1 on T =
    R/Z. Let p,q denote two multiplicatively independent numbers (no power of p equals a power of q) such as 2,3. An old result (1967) states that if E is a closed subset invariant under both f_p and f_q, then either E is all of T or it consists of a finite set of rationals. (This is far from true for a set invariant under only one transformation.) The question has been raised whether the analogous result for probability measures on T is true (known as the x2,x3 conjecture!) This question is still open, but a partial answer given by D. Rudolph treating the positive entropy case has been fruitful and has led to significant advances in homogeneous dynamics and diophantine questions. A new
    conjecture is that the f_p orbit closure and f_q orbit closure of any irrational point cannot both be small - specifically , that the sum of the Hausdorff dimensions is never < 1. We shall connect this problem with a question regarding fractals, making plausible the modified conjecture that the "dimension
    inequality" holds for all but a set of dimension 0.

  • Meromorphic differentials with real periods, and the geometry of the moduli space of curves


    Speaker: Samuel Grushevsky (Stony Brook) - http://www.math.sunysb.edu/~sam/

    When: Fri, October 4, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: We will discuss some results on the geometry of the
    moduli space of Riemann surfaces, and applications, obtained using
    meromorphic differentials with all periods real.
    These constructions are motivated by Whitham perturbation theory of
    integrable systems, and somewhat parallel to those used to study
    Teichmueller dynamics for abelian differentials.
    Based on joint work with Igor Krichever.

  • From Gene Trees to Species Trees


    Speaker: Tandy Warnow (University of Texas at Austin) - http://www.cs.utexas.edu/~tandy/

    When: Fri, September 27, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Estimating the Tree of Life will likely involve a two-step procedure, where in the first step trees are estimated on many genes, and then the gene trees are combined into a tree on all the taxa. The computational problems involved here are substantial and interesting – even if the gene trees are correctly estimated, because the individual gene trees may not include all the species, finding the true tree that contains all the species is NP-hard. Furthermore, estimated gene trees may not be correct, making the estimation problem additionally challenging. Finally, the true gene trees may not agree with each other or with the species tree, due to biological processes such as deep coalescence, gene duplication and loss, and horizontal gene transfer.
    In this talk, I will present new algorithms for these problems. The first algo- rithm is a method called SuperFine (Swenson et al., Syst Biol 2012 and Nguyen et al., J Alg Mol Biol 2012) that handles the case where there should not be con- flict between true gene trees. SuperFine is a “booster” for supertree methods, and produces highly accurate supertrees on large datasets. We then address the case where gene trees can differ form the species tree (and from each other) due to incomplete lineage sorting. For this problem, we present algorithms for the MDC (minimize deep coalescence) problem, taking gene tree estimation error into account (Yu et al., RECOMB and J Comp Biol 2011, Bayzid et al., J Comp Biol 2012). We also explore the use of “bin-and-conquer” to improve the ac- curacy and/or scalability of coalescent-based species tree methods (Bayzid and Warnow, Bioinformatics 2012).

    (By invitation of the hiring committee)

  • Rigidity and Flexibility of Schubert classes


    Speaker: Colleen Robles (IAS/Texas A&M) - http://www.math.tamu.edu/~robles

    When: Wed, September 18, 2013 - 3:15pm
    Where: Math 3206

    View Abstract

    Abstract: Consider a rational homogeneous variety X. (For example, take X to be the Grassmannian Gr(k,n) of k-planes in complex n-space.) The Schubert classes of X form a free additive basis of the integral homology of X. Given a Schubert class [S], represented by a Schubert variety S in X, Borel and Haefliger asked: aside from the Schubert variety, does [S] admit any other algebraic representatives? I will discuss this, and related questions, in the case that X is Hermitian symmetric.

  • Modeling of crystal surfaces: A journey from atoms to PDEs and back


    Speaker: Dionisios Margetis (University of Maryland) - www.math.umd.edu/~dio

    When: Wed, September 11, 2013 - 3:30pm
    Where: Math 3206

    View Abstract

    Abstract: Crystals play a critical role in the design of novel devices.
    In particular, the surface of a crystal can evolve with time and give rise to
    a variety of interesting structures used in applications. In this evolution, several length and time scales,
    from the atomistic to the continuum, are implicated; the description of their linkages poses challenging
    mathematical questions.
    How can surface evolution at large scales, possibly described by continuum laws, emerge from the motion of
    mesoscale crystal defects? And how does the description of such defects
    arise from atomistic motion? In this talk, I will address recent progress and open challenges
    in answering these questions.