Serguei NovikovIn honor of Sergei Novikov, who will be retiring shortly, the Mathematics Department at the University of Maryland announces an afternoon of talks on topics in geometric analysis by some of Novikov's distinguished students: Gennadi Kasparov (Vanderbilt University), Igor Krichever (Columbia University), and Anton Zorich (Paris Jussieu).  The event will take place on Wednesday, April 26, 2017, in William E. Kirwan Hall, University of Maryland, room 3206, and will be followed by a dinner.  All are invited to participate.

Program

Abstracts of the talks may be found here.

  • 2:00-3:00. Gennadi Kasparov, On the Novikov higher signature conjecture: history and development
  • 3:00-3:15. Tea across the hall in room 3201
  • 3:15-4:15. Igor Krichever, A discrete analog of the Novikov-Veselov hierarchy and its applications
  • 4:15-4:30. Short break
  • 4:30-5:30. Anton Zorich, Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes
  • 5:30-6:00. Presentation to Sergei in the Yorke Rotunda downstairs
  • 6:00-8:00. Buffet dinner in the Yorke Rotunda downstairs

An afternoon of geometric analysis in honor of Sergei Novikov

Titles and Abstracts

Gennadi Kasparov (Vanderbilt University), On the Novikov higher signature conjecture: history and development

(This talk is part of the Lie Groups and Representation Theory Seminar)

Abstract:  The Novikov higher signature conjecture played and continues to play an important role in the development of several areas of mathematics: topology, geometric group theory, K-theory of C*-algebras. I will give a brief exposition of the history and progress in research related with the Novikov conjecture up to the most recent results.

Igor Krichever (Columbia University), A discrete analog of the Novikov-Veselov hierarchy and its applications

(This talk is part of the Mathematics Colloquium)

Abstract:  The spectral theory of the 2D Schrödinger operator on one energy level, pioneered by Novikov and Veselov, has developed over the years is still full of open problems. In the talk I will present recent progress in this area and its application to a wide range of problems including characterization of Prym varieties in algebraic geometry and solution of a sigma SO(N) model in mathematical physics.

Anton Zorich (Institut de Mathématiques Paris-Jussieu), Equidistribution of square-tiled surfaces, meanders, and Masur-Veech volumes

(This talk is part of the Dynamics Seminar)

Abstract:  We   show  how  recent  equidistribution  results allow one to compute
approximate values of Masur-Veech volumes of the strata in the moduli spaces
of Abelian and quadratic differentials, by a Monte Carlo method.

We also show how a similar approach allows one to count the asymptotical number of
meanders  of  fixed combinatorial type in various settings in all
genera.   Our  formulae  are  particularly  efficient  for classical
meanders in genus zero.

This is joint work with V. Delecroix, E. Goujard, and P. Zograf.

 

The DelMar Numerics Day 2013 will take place Saturday May 4, 9:30am-5:30pm, in MTH 3206. The keynote speaker is Jan Hesthaven (Brown University). Registration is free. For more information, go to http://delmar.math.umd.edu.


GF-poster-red


Colloquium Lecture by Simon Donaldson: Kähler-Einstein metrics,  extremal metrics and stability
Abstract: In the first part of the talk we will give a general outline of the two topics in Kä hler geometry in the title, both growing out of work of Calabi. We will also discuss the parallels with affine differential geometry which arise when one studies toric manifolds. We will explain the standard conjectures in the field, relating the existence of these metrics to algebro-geometric notions of “stability”. In the last part of the talk we will say something about recent work with Chen and Sun which establishes this conjecture in the case of Kä hler-Einstein metrics on Fano manifolds (Yau’s conjecture).



Lecture by Brian White: Gap theorems for minimal submanifolds of spheres
Abstract: The totally geodesic k-sphere is the minimal hypersurface in the (k+1)-sphere of smallest k-dimensional area. What is the next smallest area? This is closely related to the question: what is the smallest density that a minimal variety can have at a singular point? I will discuss these questions and some sharp partial results.



Lecture by Bo Berndtsson: Variations of Bergman kernels and symmetrization of plurisubharmonic functions
Abstract: I will discuss some applications of a theorem on variation of Bergman kernels. I will concentrate on a problem concerning symmetrization of plurisubharmonic functions and generalizations of the Polya-Szegö theorem. These problems turn out to have some relations to Kähler geometry and the openness conjecture for plurisubharmonic functions. (This is mostly joint work with Robert Berman.)



Lecture by Hans-Joachim Hein: Singularities of Kähler-Einstein metrics and complete Calabi-Yau manifolds
Abstract: When Einstein metrics form singularities one expects to see a bubble tree structure in which the bubbles are complete Ricci-flat spaces. We still lack a detailed understanding of this process in general. I will discuss several examples - old, new, and speculative - of singularity formation in the Kähler-Einstein case. Topics will include gravitational instantons in real dimension 4, and isolated Einstein singularities whose tangent cones have nonisolated singularities. Partly joint with Ronan Conlon and Aaron Naber.



Lecture by Andrea Malchiodi: Uniformization of surfaces with conical singularities
Abstract: We consider a class of singular Liouville equations which arise from the problem of prescribing the Gaussian curvature of a surface imposing a given conical structure at a finite number of points (as well as from models in Chern-Simons theory). The problem is variational, and differently from the "regular" case the Euler-Lagrange functional might be unbounded from below. We will look for critical points of saddle type using a combination of improved geometric inequalities and topological methods. This is joint work with D. Bartolucci, A. Carlotto, F. De Marchis and D. Ruiz.




Special Lecture by Eugenio Calabi



Lecture by Yuval Peres: The geometry of fair allocation to random points
Abstract: Given a random scatter of points (obtained as a limit of uniform picks from a large cube, or as the zeros of a random analytic function) , our goal is to allocate to each point of the process a unit of volume, in a deterministic translation-invariant way, so that the diameter of the region allocated to each point is stochastically as small as possible. One approach to this problem, studied in joint work with C. Hoffman and A. Holroyd, uses the stable marriage algorithm of Gale and Shapley. In  dimensions 3 and higher, gravity without inertia yields a satisfying solution.  The fairness of the allocation is a consequence of the divergence theorem; The diameters of the allocated regions are analyzed using methods from percolation theory.  Finally, I will relate the properties of the allocation to rigidity properties of the underlying point process.
References:
Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval A stable marriage of Poisson and Lebesgue.Ann. Probab. 34 (2006), no. 4, 1241–1272.
Nazarov, Fedor; Sodin, Mikhail; Volberg, Alexander Transportation to random zeroes by the gradient flow. Geom. Funct. Anal. 17 (2007), no. 3, 887–935.
Chatterjee, Sourav; Peled, Ron; Peres, Yuval; Romik, Dan Gravitational allocation to Poisson points. Ann. of Math. (2) 172 (2010), no. 1, 617–671.
Subhro Ghosh and Yuval Peres, Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues. Preprint (2013), arXiv:1211.2381



[no video]
Lecture by Aaron Naber: Characterizations of bounded Ricci curvature and applications
Abstract:  The purpose of this talk is two-fold. First we give new ways of characterizing bounded Ricci curvature on a smooth metric measure space (Mn,g,e-fdvg). In essence, we show that bounded Ricci curvature controls the infinite dimensional analysis on the path space P(M) of a manifold in a manner analogous to how lower Ricci curvature controls the analysis on M. In particular, we show that the Ornstein-Uhlenbeck operator L on the based path space Px,T(M)= {γ:[0,T] → M; γ(0)=x}, which is a form of infinite dimensional Laplacian, has a spectral gap of (ekT+1)/2 if and only if the Bakry-Emery-Ricci curvature Rc+∇2f is bounded by k. Similarly the Ornstein-Uhlenbeck operator has a log-Sobolev constant of ekT+1 iff the Ricci curvature is bounded by k. We have many other characterizations as well, including notions which relate the Wasserstein geometry of the space of probability measures on M to the metric-measure geometry of path space, and including notions analagous to dimensional Ricci curvature bounds which control |Rc+∇2f-(1/(N-n))∇ f⊗ ∇ f|. In the second part of the talk we build the necessary tools in order to use these new characterizations to define bounded Ricci curvature on an essentially arbitrary metric measure space (X,d,v). The primary technical difficulty is to describe the right notion of parallel translation invariant vector fields along continuous curves in such a setting.  Even on a smooth manifold this requires deep ideas from stochastic analysis, but we provide a new approach even in this context which generalizes to arbitrary metric spaces. We spend some time discussing the structure of metric measure spaces with generalized bounded Ricci curvature. In particular we show its possible to define the Ornstein-Uhlenbeck operator on their path spaces, and that these operators also have the desired analytic control proven on smooth spaces. We also show spaces with generalized Ricci curvature bounded by k in this new sense have lower Ricci curvature bounded from below by -k in the sense of Lott-Villani-Sturm.



Lecture by Peter Kronheimer: Instanton homology for knots and webs
Abstract: Andreas Floer introduced instanton homology for 3-manifolds in the mid 1980's. He also described a variant he called knot homology, for knots in 3-manifolds. There has now been a lot of progress in understanding the structure of instanton knot homology and its relationship with other, more recent invariants of knots, such as Khovanov homology. Applications have included a proof that Khovanov homology detects the unknot. Replacing the Lie group SU(2) in Floer's construction with SU(N) for larger N leads to an invariant of "webs" (labeled trivalent graphs), with a connection to Khovanov-Rozansky homology. This talk will review some of these developments.

Subcategories

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018

  • Math Department Welcome

    Speaker: () -

    When: Wed, September 13, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Approximation Algorithms: Some ancient, some new - the good, the bad and the ugly

    Speaker: Samir Khuller (University of Maryland Computer Science ) - https://www.cs.umd.edu/users/samir/

    When: Wed, September 20, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: NP-complete problems abound in every aspect of our daily lives. One approach is to simply deploy heuristics, but for many of these we do not have any idea as to when the heuristic is effective and when it is not. Approximation algorithms have played a major role in the last three decades in developing a foundation for a better understanding of optimization techniques - greedy algorithms, algorithms based on LinearProgramming (LP) relaxations have paved the way for the design of (in some cases) optimal heuristics. Are these the best ones to use in “typical” instances? Maybe, maybe not.


    In this talk we will focus on two specific areas - one is in the use of greedy algorithms for a basic graph problem called connected dominating set, and the other is in the development of LP based algorithms for a basic scheduling problem in the context of data center scheduling.
  • Faculty Meeting with CMNS Interim Dean, Jerry Wilkinson

    Speaker: (CMNS Dean's Office) -

    When: Wed, September 27, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Binet-Legendre metric and applications of Riemannian results in Finsler geometry

    Speaker: Vladimir Matveev (Friedrich-Schiller-Universität Jena ) - http://users.minet.uni-jena.de/~matveev/

    When: Wed, October 4, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We introduce a construction that associates a Riemannian metric $g_F$ (called the
    Binet-Legendre metric) to a
    given Finsler metric $F$ on a smooth manifold $M$. The transformation
    $F \mapsto g_F$ is $C^0$-stable and has good
    smoothness properties, in contrast to previously considered
    constructions. The Riemannian metric $g_F$ also behaves nicely under
    conformal or isometric transformations of the Finsler metric $F$ that
    makes it a powerful tool in Finsler geometry. We illustrate that by
    solving a number of named problems in Finsler geometry. In particular
    we extend a classical result of Wang to all dimensions. We answer a
    question of Matsumoto about local conformal mapping between two
    Berwaldian spaces and use it to investigation of essentially conformally Berwaldian manifolds.
    We describe all possible conformal self maps and all self similarities
    on a Finsler manifold, generasing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat
    Finsler manifolds. We solve a conjecture of Deng and Hou on locally
    symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new ``easy to calculate''
    conformal and metric invariants of finsler manifolds.
    The results are based on the papers arXiv:1104.1647, arXiv:1409.5611,
    arXiv:1408.6401, arXiv:1506.08935,
    arXiv:1406.2924
    partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne).
  • (No colloquium)

    Speaker: General Departmental Meeting () -

    When: Wed, October 11, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • No colloquium

    Speaker: Departmental Meeting () -

    When: Wed, October 18, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • No colloquium

    Speaker: Departmental Meeting () -

    When: Wed, October 25, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Some results on affine Deligne-Lusztig varieties

    Speaker: Xuhua He (UMD) - http://www.math.umd.edu/~xuhuahe/

    When: Wed, November 1, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: In Linear Algebra 101, we encounter two important features of the group of invertible matrices: Gauss elimination method, or the LU decomposition of almost all matrices, which is an important special case of the Bruhat decomposition; the Jordan normal form, which gives a classification of the conjugacy classes of invertible matrices.

    The study of the interaction between the Bruhat decomposition and the conjugation action is an important and very active area. In this talk, we focus on the affine Deligne-Lusztig variety, which describes the interaction between the Bruhat decomposition and the Frobenius-twisted conjugation action of loop groups. The affine Deligne-Lusztig variety was introduced by Rapoport around 20 years ago and it has found many applications in arithmetic geometry and number theory.

    In this talk, we will discuss some recent progress on the study of affine Deligne-Lusztig varieties, and some applications to Shimura varieties.
  • Quantitative estimates of propagation of chaos for large systems of interacting particles

    Speaker: Pierre-Emmanuel Jabin (UMD) - http://www2.cscamm.umd.edu/~jabin/

    When: Wed, November 8, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We present a new method to derive quantitative estimates proving the propagation of chaos for large stochastic or deterministic systems of interacting particles. Our approach requires to prove large deviations estimates for non-continuous potentials modified by the limiting law. But it leads to explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit; and it can be applied to very singular kernels that are only in negative Sobolev spaces and include the Biot-Savart law for 2d Navier-Stokes
  • Scale, pattern and biodiversity

    Speaker: Simon Levin (Princeton ) -

    When: Wed, November 15, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: One of the deepest problems in ecology is in understanding how so many species coexist, competing for a limited number of resources. This motivated much of Darwin’s thinking, and has remained a theme explored by such key thinkers as Hutchinson (“The paradox of the plankton”), MacArthur, May and others. A key to coexistence, is in the development of spatial and spatio-temporal patterns, and in the coevolution of life-history patterns that both generate and exploit spatio-temporal heterogeneity. Here, general theories of pattern formation, which have been prevalent not only in ecology but also throughout science, play a fundamental role in generating understanding. The interaction between diffusive instabilities, multiple stable basins of attraction, critical transitions, stochasticity and far-from-equilibrium phenomena creates a broad panoply of mechanisms that can contribute to coexistence, as well as a rich set of mathematical questions and phenomena. This lecture will cover as much of this as time allows.
  • Math Teaching Forum

    Speaker: () -

    When: Fri, November 17, 2017 - 3:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Our lecturers Hilaf Hasson, Kendall Williams and Allan Yashinski will be hosting the panel on the realities of teaching. The target audience first includes Math TAs but we are hoping to attract many in the department. Light refreshments to follow in room 3201.
  • Ergodic properties of parabolic systems.

    Speaker: Adam Kanigowski

    When: Wed, November 29, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Parabolic dynamical systems are systems of intermediate (polynomial) orbit growth. Most important classes of parabolic systems are: unipotent flows on homogeneous spaces and their smooth time changes, smooth flows on compact surfaces, translation flows and IET's (interval exchange transformations). Since the entropy of parabolic systems is zero, other properties describing chaoticity are crucial: mixing, higher order mixing, decay of correlations.
    One of the most important tools in parabolic dynamics is the Ratner property (on parabolic divergence), introduced by M. Ratner in the class of horocycle flows. This property was crucial in proving famous Ratner's rigidity theorems in the above class.

    We will introduce generalisations of Ratner's property for other parabolic systems and discuss it's consequences for chaotic properties. In particular this allows to approach the Rokhlin problem in the class of smooth flows on surfaces and in the class of smooth time changes of Heisenberg nilflows.
  • Mobius disjointness for some dynamical systems of controlled complexity

    Speaker: Zhiren Wang

    When: Wed, December 6, 2017 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Sarnak's Mobius disjointness conjecture speculates that the Mobius sequence is disjoint to all topological dynamical systems of zero topological entropy. We will survey the recent developments in this area, and discuss several special classes of dynamical systems of controlled complexity that satisfy this conjecture. Part of the talk is based on joint works with Wen Huang, Xiangdong Ye, and Guohua Zhang. No background knowledge in either dynamical systems or number theory will be assumed.

  • Dimension gaps in self-affine sponges

    Speaker: David Simmons (University of York) -

    When: Thu, December 7, 2017 - 2:00pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Abstract: In this talk, I will discuss a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension, as well as my recent result showing that the answer is negative. The counterexample is a self-affine sponge in $\mathbb R^3$ coming from an affine iterated function system whose coordinate subspace projections satisfy the strong separation condition. Its dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, which implies that sponges with a dimension gap represent a nonempty open subset of the parameter space. This work is joint with Tushar Das (Wisconsin -- La Crosse).
  • TBA (Douglas Lecture)

    Speaker: Daniel Tataru (UC Berkeley) - https://math.berkeley.edu/~tataru/

    When: Fri, December 8, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Taking Mathematics to Heart

    Speaker: Alfio Quarteroni (Politecnico di Milano, Milan, Italy and EPFL, Lausanne, Switzerland ) - https://cmcs.epfl.ch/people/quarteroni

    When: Fri, February 2, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Abstract : In this presentation I will highlight the great potential offered by the interplay between data science and computational science to efficiently solve real life large scale problems . The leading application that I will address is the numerical simulation of the heart function.

    The motivation behind this interest is that cardiovascular diseases unfortunately represent one of the leading causes of death in Western Countries.

    Mathematical models based on first principles allow the description of the blood motion in the human circulatory system, as well as the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical environment where multi-physics processes have to be addressed.


    Appropriate numerical strategies can be devised to allow for an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimization of assisted devices or surgical prostheses.

    This presentation will address some of these issues and a few representative applications of clinical interest.
  • Defects in periodic homogenization problems : Toward a complete theory [Appl Math Colloquium]

    Speaker: Claude Le Bris (Ecole des Ponts and Inria) - https://cermics.enpc.fr/~lebris/

    When: Tue, February 6, 2018 - 3:30pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We will present some recent mathematical contributions related to nonperiodic homogenization problems. The difficulty stems from the fact that the medium is not assumed periodic, but has a structure with a set of embedded localized defects, or more generally a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct a theoretical setting providing an efficient and accurate approximation of the solution. The questions raised ranged from the theory of elliptic PDEs, homogenization theory to harmonic analysis and singular operators.
  • Aziz Lecture

    Speaker: Claude Le Bris () -

    When: Wed, February 7, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Spectral analysis on singular spaces

    Speaker: Alexander Teplyaev (University of Connecticut) - http://teplyaev.math.uconn.edu

    When: Fri, February 9, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: The talk will outline recent achievements and challenges in spectral and stochastic analysis on non-smooth spaces that are very singular, but can be approximated by graphs or manifolds. In particular, the talk will present two of most interesting examples that are currently
    under investigation. One example deals with the spectral analysis of the Laplacian on the famous basilica Julia set, the Julia set of the polynomial z^2-1. This is a joint work with Luke Rogers and several students at UConn. The other example deals with spectral, stochastic, functional analysis for the canonical diffusion on the pattern spaces of an aperiodic Delone set. This is a joint work with Patricia Alonso-Ruiz, Michael Hinz and Rodrigo Trevino.
  • Stability for symmetric groups and Hecke algebras

    Speaker: Weiqiang Wang (University of Virginia) Abstract: We will describe a certain stability for the centers of the group algebras of the symmetric groups S_n for varying n, and its geometric counterpart. (To experts: this is not about Schubert calculus). We shall then explain the generalization of this stability phenomenon for wreath products and for Hecke algebras. This talk should be accessible to graduate students.

    When: Wed, February 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: We will describe a certain stability for the centers of the group algebras of the symmetric groups S_n for varying n, and its geometric counterpart. (To experts: this is not about Schubert calculus). We shall then explain the generalization of this stability phenomenon for wreath products and for Hecke algebras. This talk should be accessible to graduate students.
  • Alpha invariants and birational geometry.

    Speaker: Ivan Cheltsov (University of Edinburgh, UK) - http://www.maths.ed.ac.uk/cheltsov/Abstract: Tian introduced alpha invariants to study the existence ofKahler-Einstein metrics on Fano manifolds.In this talk we describe (explicit and implicit) appearance of alphainvariants in (global and local) birational geometry.

    When: Wed, February 21, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Tian introduced alpha invariants to study the existence ofKahler-Einstein metrics on Fano manifolds.In this talk we describe (explicit and implicit) appearance of alphainvariants in (global and local) birational geometry.
  • Nonlinear fluid-structure interaction with fiber-reinforced soft composites: a unified mathematical framework for mathematical analysis, computation and applications

    Speaker: Suncica Canic (University of Houston) - https://www.math.uh.edu/~canic/

    When: Fri, February 23, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.
    Mathematically, these problems give rise to a class of highly nonlinear, moving- boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub- problems. In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information. Examples of applications in coronary angioplasty and micro- swimmer biorobot design will be shown.
  • TBA

    Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/

    When: Wed, March 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Richard Montgomery (UCSC) - https://people.ucsc.edu/~rmont/

    When: Wed, March 28, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Spring Teaching forum

    Speaker: Teaching forum () -

    When: Wed, April 11, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Shrawan Kumar (UNC at Chapel Hill) - http://www.unc.edu/math/Faculty/kumar/

    When: Wed, April 18, 2018 - 3:15pm
    Where: Kirwan Hall 3206

    View Abstract

    Abstract: TBA
  • TBA

    Speaker: Alexander Vladimirsky (Cornell University) - http://www.math.cornell.edu/~vlad/

    When: Wed, April 25, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: TBA Kirwan Lecture () -

    When: Fri, April 27, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Lillian Pierce (Duke University/IAS) - https://services.math.duke.edu/~pierce/

    When: Wed, May 2, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA (Aziz)

    Speaker: Arnaud Debussche (ENS, Rennes, France) - http://w3.ens-rennes.fr/math/people/arnaud.debussche/

    When: Fri, May 4, 2018 - 3:15pm
    Where: Kirwan Hall 3206