Colloquium Archives for Academic Year 2015


Hodge Theory on Matroids

When: Wed, September 9, 2015 - 3:15pm
Where: Math 3206
Speaker: Eric Katz (Univerisity of Waterloo) - http://www.math.uwaterloo.ca/~eekatz/
Abstract: The chromatic polynomial of a graph counts its proper colourings. This polynomial's coefficients were conjectured to form a unimodal sequence by Read in 1968. This conjecture was extended by Rota in his 1970 address to assert the log-concavity of the characteristic polynomial of matroids which are the common generalizations of graphs and linear subspaces. We discuss the resolution of this conjecture which is joint work with Karim Adiprasito and June Huh. The solution draws on ideas from the theory of algebraic varieties, specifically Hodge theory, showing how a question about graph theory leads to a solution involving Grothendieck's standard conjectures.

Galileo's New Mathematics

When: Wed, September 16, 2015 - 3:15pm
Where: Math 3206
http://www2.math.umd.edu/~pbrosnan/Speaker: Mark A. Peterson (Mount Holyoke College) - https://www.mtholyoke.edu/acad/facultyprofiles/mark_peterson
Abstract: Galileo isn't really remembered for his mathematics.
There is nothing called "Galileo's Theorem," for instance.
But Galileo did make a fundamental contribution to mathematics,
arguably more important than any new theorem, namely a new (or re-discovered)
conception of what mathematics could mean. In the decades before
Galileo, higher mathematics was an essentially static and obscure
corner of philosophy, barely connected to physical reality.
After Galileo, mathematics became the scaffolding
of physics, and (apparently as a consequence) subject to rapid development.
This revolution in Galileo's thought, and in the philosophy of
mathematics more generally, had to come from outside mathematics:
in Galileo's case it had its roots in literature, the arts, and quite
possibly the theology of the High Middle Ages.

Colloquium supeseded by Math Department Welcome

When: Fri, September 25, 2015 - 3:15pm
Where: Math 3206
Speaker: Math Department Welcome () -


Milnor-Witt K-Theory

When: Wed, October 14, 2015 - 3:15pm
Where: Math 3206
Speaker: Stefan Gille (Alberta) -
http://www.math.ualberta.ca/~gille/
Abstract: Milnor-Witt K-theory arises in the Morel-Voevodsky homotopy theory over a field and plays a role in the classification of vector bundles over smooth schemes. Morel in collaboration with Hopkins discovered a nice presentation of these groups, which has been recently generalized by Changlong Zhong, Stephen Scully and myself to semilocal rings which contain an infinite field. In my talk I will discuss this result and also present some applications of these groups.

No Seminar

When: Wed, October 21, 2015 - 3:15pm
Where: Math 3206
Speaker: No Seminar () -


No Seminar

When: Wed, October 28, 2015 - 3:15pm
Where: Math 3206
Speaker: No Seminar () -


No Colloquium

When: Fri, October 30, 2015 - 3:15pm
Where: Math 3206
Speaker: No Colloquium () -


John Horvath remembrance event

When: Wed, November 4, 2015 - 3:15pm
Where: Math 3206
Speaker: Hold Date () -


Geometry of ODE's with a small parameter

When: Wed, November 11, 2015 - 3:15pm
Where: 3206.0
Speaker: Dima Arinkin (University of Wisconsin) - http://www.math.wisc.edu/~arinkin/
Abstract: I will look at very classical objects (linear ordinary differential equations) and study them from the view-point of algebraic geometry. The starting point is some simple results about differential operators of the form h(d/dx)+A(x), where h is small. The results lead to a non-trivial and beautiful picture for the parameter space of such equations, which may be interpreted geometrically as the moduli space of bundles with connections on a Riemann surface.

Tensor Sparsity - a Regularity Notion for High Dimensional PDEs [Aziz Lecture]

When: Wed, November 18, 2015 - 3:15pm
Where: Math 3206
Speaker: Wolfgang Dahmen (Aachen University, Germany) - https://www.igpm.rwth-aachen.de/personen/dahmen
Abstract: The numerical solution of PDEs in a spatially high-dimensional regime (such as the electronic Schrodinger or Fokker-Planck
equations) is severely hampered by the "curse of dimensionality":
the computational cost required for achieving a desired target accuracy increases exponentially with respect to the spatial dimension.

We explore a possible remedy by exploiting a typically hidden sparsity of the solution to such problems with respect to a problem dependent basis or dictionary. Here sparsity means that relatively few terms from such a dictionary suffice to realize a given target accuracy. Specifically, sparsity with respect to dictionaries comprised of separable functions -- rank-one tensors
-- would significantly mitigate the curse of dimensionality. The main result establishes such tensor-sparsity for elliptic problems over product domains when the data are tensor-sparse, which can be viewed as a structural regularity theorem.


A drunk walk in a drunk world

When: Wed, December 9, 2015 - 3:15pm
Where: Math3206
Speaker: Ivan Corwin (Columbia University, Clay Mathematics Institute) - http://www.math.columbia.edu/~corwin/
Abstract: In a simple symmetric random walk on Z a particle jumps left or right with 50% chance independently at each time and space location. What if the jump probabilities are taken to be random themselves (e.g. uniformly distributed between 0% and 100%). In this talk we will describe the effect of this random environment on a random walk, in particular focusing on a new connection to the Kardar-Parisi-Zhang universality class and to the theory of quantum integrable systems. No prior knowledge or background will be expected.

ENIGMA: Harnessing mathematics in cryptology

When: Fri, January 29, 2016 - 3:15pm
Where: Math 3206
Speaker: Roman Sznajder (Bowie State University) - http://www.bowiestate.edu/academics-research/faculty-staff-directory/details/sznajder/
Abstract: ENIGMA was a German ciphering machine developed soon after WWI for commercial use. Shortly after, it was acquired by the German army and used for encrypting and decrypting military messages and orders. We discuss the circumstances that led to the initial breaking of the Enigma code in 1932 by three young cryptologists: Rejewski, Różycki, and Zygalski from the Polish Cipher Office. This was the first time when mathematics was systematically used in cryptography. Specifically, there were applications of permutation groups used to reconstruct the wiring of military Enigma and then to recover the daily keys and keys for individual messages. In the summer of 1939, when the outbreak of WWII was imminent, the Polish Cipher Office provided Allies with two copies of the Enigma machine and daily keys. Aided by these materials, the British immediately began working on breaking Enigma messages. Their office in Bletchley Park had access to human, engineering, and technological resources on an industrial scale. The ability to read encrypted messages used by the German army—enabled by the breaking of the Enigma code—contributed to the shortening of WWII and, according to some estimates, spared several million lives. With the British WWII archives sealed and Poland behind the Iron Curtain, the British Secret Service suppressed the knowledge about the role of Polish intelligence in breaking the Enigma code for about thirty years. The heroic effort of three Polish cryptologists was virtually unknown to the world until the 1973 publication of a book by the French general Gustave Bertrand. In this presentation, we will shed some light on mathematical methods, the events and people involved in the successful effort to break the Enigma code.

p-adic uniformization of Shimura curves

When: Wed, February 10, 2016 - 3:15pm
Where: Math 3206
Speaker: Michael Rapoport (Universitaet Bonn ) - http://www.math.uni-bonn.de/ag/alggeom/rapoport
Abstract: Shimura curves are algebraic curves that arise through complex
uniformization by an arithmetic group acting on the complex half
plane. Forty years ago, Cherednik observed that under suitable
assumptions, these curves can also be uniformized by the Drinfeld
p-adic half plane. Now we are close to a reasonable proof (of a
variant) of this statement.
I will report on joint work with S. Kudla and Th. Zink, and related
work of P. Scholze.

Equidistribution of Frobenius eigenvalues

When: Fri, February 12, 2016 - 3:15pm
Where: 3206.0
Speaker: Kiran Kedlaya (UCSD) -
Abstract: Consider a system of polynomial equations with integer coefficients. For
each prime number p, one can count the solutions of these equtaions in
the integers modulo p; while the structure of these counts is a rather
deep topic in number theory, one can pose statistical questions about
these counts for which the answers are expected to be somewhat simpler
(although still deep). We discuss several variations on this theme,
including the Chebotarev density theorem, the Sato-Tate conjecture for
elliptic curves, a general but imprecise conjecture of Serre, and a
precise form of Serre's conjecture for genus 2 curves due to
Fite-Kedlaya-Rotger-Sutherland.


Singularity formation in nonlinear PDE’s: a qualitative approach

When: Wed, February 17, 2016 - 11:00am
Where: Math 3206
Speaker: Pierre Raphael (U. Nice Sophia Antipolis) - http://math.unice.fr/~praphael/
Abstract: The qualitative study of nonlinear partial differential equations has made spectacular progress in the past 30 years. Various deep nonlinear phenomenons have now been exhibited, at least on some canonical simplified models extracted from physics. I shall report in this talk onto one specific phenomenon: singularity formation, and more generally energy concentration. I will illustrate on some canonical models (like the seminlinear heat or Schrodinger equation) how one can construct and completely understand some scenarios of energy concentration, and how a complete classification of such blow up dynamics can sometimes be obtained. At the heart of the analysis lies a fundamental nonlinear object: the solitary wave.

Geometric graph-based methods for high dimensional data

When: Fri, February 19, 2016 - 3:15pm
Where: MTH 3206
Speaker: Andrea Bertozzi (UCLA) - http://www.februaryfouriertalks.com
Abstract: Special Department Colloquium part of the 2016 February Fourier Talks.

Registration and full schedule of talks at www.februaryfouriertalks.com

Abstract:
We present new methods for segmentation of large datasets with graph based structure. The method combines ideas from classical nonlinear PDE-based image segmentation with fast and accessible linear algebra methods for computing information about the spectrum of the graph Laplacian. The goal of the algorithms is to solve semi-supervised and unsupervised graph cut optimization problems. I will present results for image processing applications such as image labeling and hyperspectral video segmentation, and results from machine learning and community detection in social networks, including modularity optimization posed as a graph total variation minimization problem.

Global controllability to trajectories for the viscous Burgers equation

When: Wed, February 24, 2016 - 3:15pm
Where: 3206.0
Speaker: Armen Shirikyan (Université de Cergy-Pontoise ) - http://shirikyan.u-cergy.fr
Abstract: We study the problem of global controllability by an external force for the viscous Burgers equation on a bounded interval. Assuming that the force is localised in space, we prove that any non-stationary trajectory can be exponentially stabilised. We next discuss various consequences of this result, including global exact controllability to trajectories and approximate controllability by a localised low-dimensional control.

Arithmetic properties of function fields of p-adic curves

When: Fri, February 26, 2016 - 3:15pm
Where: Math 3206
Speaker: R. Parimala (Emory ) - http://www.mathcs.emory.edu/~parimala/
Abstract: Classical theorems over number fields like the Hasse-Minkowski theorem
on local-global principles for zeros of quadratic forms have
surprising analogues over function fields of p-adic curves. We will
expand on some results in this direction and also discuss several open
questions concerning homogeneous spaces under connected linear
algebraic groups over such fields.

Discussion with EPSL Head Librarian

When: Wed, March 2, 2016 - 3:15pm
Where: Math 3206
Speaker: Nevenka Zdravkovska (UMCP Libraries) - http://www.lib.umd.edu/epsl/contact-epsl/profile_zdravkovska


Combinatorics to Geometry to Arithmetic of Circle Packings

When: Fri, March 4, 2016 - 3:15pm
Where: Math 3206
Speaker: Alex Kontorovich (Rutgers University) - http://www.math.rutgers.edu/~ak1230/index.html
Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a
conformally rigid circle packing to a convex polyhedron; for example,
the tetrahedron is mapped to the classical Apollonian Circle Packing.
The latter, an object of much recent study, is "arithmetic", in that
there are configurations for which all circles have curvatures in the
rational integers. Our aim, in joint work with Kei Nakamura, is to
classify polyhedra with this property. We will start from scratch and
report on work in progress towards this goal.

Asymptotic limits for collisional kinetic equations

When: Mon, March 7, 2016 - 11:00am
Where: Math 3206
Speaker: Marjolaine Puel (Université de Nice-Sophia-Antipolis) - http://math.unice.fr/laboratoire/equipes-de-recherche/edp-et-analyse-num%C3%A9rique
Abstract: In several domain of applied math as nuclear industry, aerodynamic, biology, gas dynamics may be modeled by some kinetic equations. Their structure is complex and a real challenge consists in providing simpler models that are more performant for numerics.
We first try to explain how kinetic equations may be linked to particle trajectories and introduce two particular cases, the Boltzmann equation and the Fokker Planck equation. Then we will give the context in which kinetic equations may be approximated by more macroscopic equations. At the end, we will focus on the diffusion approximation and in particular on the anomalous diffusion approximation for both Boltzmann and Fokker Planck.

Hypoelliptic Laplacian and probability

When: Wed, March 9, 2016 - 3:05pm
Where: 3201.0
Speaker: Jean-Michel Bismut (Université Paris-Sud) - http://www.math.u-psud.fr/~bismut/Web_page_of_Jean-MThe hypoelliptic Laplacian is a family of operators, indexed by b in R*_+ ,
acting on the total space of the tangent bundle of a Riemannian manifold, that
interpolates between the ordinary Laplacian as b tends to 0 and the generator of the
geodesic ow as b tends to infinity . The probabilistic counterpart to the hypoelliptic
Laplacian is a 1-parameter family of dierential equations, known as geometric
Langevin equations, that interpolates between Brownian motion and the geodesic
I will present some of the probabilistic ideas that explain some of its remarkable
and often hidden properties. I will also explain some of the applications of
the hypoelliptic Laplacian that have been obtained so far.ichel_Bismut/Contact_information.html
Abstract: The hypoelliptic Laplacian is a family of operators, indexed by b in R*_+ ,
acting on the total space of the tangent bundle of a Riemannian manifold, that
interpolates between the ordinary Laplacian as b tends to 0 and the generator of the
geodesic ow as b tends to infinity . The probabilistic counterpart to the hypoelliptic
Laplacian is a 1-parameter family of dierential equations, known as geometric
Langevin equations, that interpolates between Brownian motion and the geodesic
I will present some of the probabilistic ideas that explain some of its remarkable
and often hidden properties. I will also explain some of the applications of
the hypoelliptic Laplacian that have been obtained so far.

Department Meeting

When: Wed, March 30, 2016 - 3:15pm
Where: Math 3206
Speaker: Department Meeting (UMCP) -


The static and dynamical Ising and Potts models

When: Wed, April 6, 2016 - 3:15pm
Where: Math 3206
Speaker: Eyal Lubetzky (NYU) - http://cims.nyu.edu/~eyal/
Abstract: The Ising model, one of the most studied models in mathematical physics, was introduced in 1925 to model ferromagnetism. In the classical 2D setting, the model assigns plus/minus spins to the sites of the square grid according to a given probability distribution, which is a function of the number of neighboring sites whose spins agree, as well as the temperature. The Potts model is its generalization into q>2 possible values for each site. Over the last three decades, significant effort has been dedicated to the analysis of stochastic dynamical systems that both model the evolution of the Ising and Potts models, and provide efficient methods for sampling from it. In this talk I will survey the rich interplay between the behaviors of the static and the dynamical models, as they both undergo a phase transition at a critical temperature.

Artificial Intelligence and data science from Eric Horvitz (Microsoft) and DJ Patil (White House)

When: Fri, April 8, 2016 - 9:00am
Where: Time and Place to be determined


Department Meeting

When: Fri, April 8, 2016 - 3:15pm
Where: Math 3206
Speaker: Department Meeting (UMD) -


The Rigorous Derivation of the Focusing NLS from Quantum Many-body Evolution

When: Wed, April 13, 2016 - 3:15pm
Where: 3206.0
Speaker: Xuwen Chen (Brown University) http://www.math.brown.edu/~chenxuwen/
Abstract:The rigorous justification of mean-field type equations (Boltzmann, Vlasov-Poisson, NLS...) from the many-body systems they are supposed to describe is a vast and fundamental subject. In this talk, we talk about recent advances in this area on the derivation of focusing nonlinear Schrodinger equations (NLS) from quantum many-body evolutions in the context of Bose-Einstein condensation, which has been one of the most active areas of contemporary research since the Nobel prize winning experiments. We survey the background and the evolution of the results and techniques in the field during the talk.



Smooth surface diffeomorphisms and their invariant probability measures

When: Fri, April 15, 2016 - 3:15pm
Where: Math 3206
Speaker: Jerome Buzzi (Orsay) - http://www.math.u-psud.fr/~buzzi/
Abstract: A classical result of Katok shows that surface
diffeomorphisms are approximated by horseshoes with respect to
topological entropy. From a recent result of Hochman, one obtains a
Borel conjugacy to a Markov shift respecting all invariant ergodic
probability measures except possibly for measures with zero entropy
and measures maximizing the entropy at their periods. I will explain
what joint works with Boyle and with Crovisier and Sarig say (and
don't say) about these latter measures and present some open
problems.

CANCELLED! (Interpretations of Probability)

When: Wed, April 20, 2016 - 3:15pm
Where: Math 3206
Speaker: Aidan Lyon (UMCP Philosophy) - http://aidanlyon.com/
Abstract: The concept of probability plays a crucial role in every branch of science and everyday life. Indeed, probability is so important to all of humanity's endeavors that Bishop Butler once said that "probability is the very guide to life" and Henri Poincaré once wrote that “if [the probability] calculus be condemned, then the whole of the sciences must also be condemned”. However, despite the ubiquity and importance of the concept of probability, it is surprisingly difficult to say what statements of probability mean. What do we mean when we say something has a particular probability? To answer this question is to give an interpretation of probability. In this talk, I will give a critical overview of the leading interpretations of probability: the classical, logical, frequentist, propensity, subjective, and best-system interpretations of probability.

A sharp counter example to local existence for Einstein equations in wave coordinates

When: Fri, April 22, 2016 - 3:15pm
Where: Math 3206
Speaker: Hans Lindblad (Hopkins) - http://www.math.jhu.edu/~lindblad/
Abstract: We are concerned with how regular initial data have to be to ensure local existence for Einstein's equations in wave coordinates. Klainerman-Rodnianski and Smith-Tataru showed that there in general is local existence for data in H^s for s>2. We give example of data in H^2 for which there is no local solution in H^2. This is joint work with Boris Ettinger.

Polterovich ``Billiards with a large Weyl remainder''

When: Wed, April 27, 2016 - 3:15pm
Where: Math3206
Speaker: Iosif Polterovich (Université de Montréal) - http://www.dms.umontreal.ca/~iossif/

The classical Hardy-Landau lower bound for the error term in the Gauss
circle problem can be viewed as an estimate from below for the remainder in
Weyl's law for the eigenvalue counting function on a torus. In the talk we
will present an analogous estimate for certain planar domains admitting an
appropriate one-parameter family of periodic billiard trajectories. Examples
include ellipses and smooth domains of constant width. In higher dimensions, lower bounds on the remainder in Weyl's law are of somewhat different nature, and they will be discussed as well. The talk is based on a joint work with S. Eswarathasan and J. Toth.

Held for Department Meeting

When: Fri, April 29, 2016 - 3:15pm
Where: Math 3206
Speaker: Department Meeting (UMD) -


Aziz Lecture- TBA

When: Wed, May 4, 2016 - 3:15pm
Where: Math 3206
Speaker: Irene Fonseca (Carnegie Mellon University) - http://www.math.cmu.edu/math/faculty/fonseca


Held for Department Meeting

When: Fri, May 6, 2016 - 3:15pm
Where: Math 3206
Speaker: Department Meeting (UMD) -