Organizers: Richard Wentworth (Math), Tristan Hubsch (Physics, Howard Univ.), Jonathan Rosenberg (Math), Amin Gholampour (Math)
Other Faculty Participants: Joel Cohen (Math), Paul Green (Math, emeritus)
When: Thursdays @ 3:30pm-4:30pm
Where: PHY 1117 (This is the Center for Particle & String Theory, located in what used to be the physics chair's office in the Toll Physics Building adjacent to the Mathematics department.)

This interdisciplinary RIT will aim to foster interactions between mathematicians and physicists on topics of mutual interest.  It will roughly follow the example of a similar RIT from 2010-2011 and from the last three years. The topic for 2016-17 was mirror symmetry.

It is not assumed that participants already be knowledgeable in both math and physics, just in some aspect of one or the other. Relevant math topics are differential geometry, representation theory, algebraic topology, and algebraic geometry. Relevant physics topics are classical and quantum field theories, and supersymmetry.

The organization meeting for Fall 2017 is scheduled for September 7th. Students (advanced undergraduates or graduate students) who want to participate can get credit as MATH 489 (undergrad) or 689 (graduate) if they wish, by contacting the organizers.

We have a wiki where participants can exchange comments and revise notes.  Contact the math/physics computer helpdesk if you need a login id and password.

 Topics from previous years:

  1. Supermanifolds, topology, and integration --- a few references:
    • S. J. Gates, Ectoplasm has no topology, hep-th/9709104 and hep-th/9809056.
    • E. Witten, Notes On Supermanifolds and Integration1209.2199.
    • The Berezin integral.
    • S. J. Gates and G. Tartaglino-Mazzucchelli, Ectoplasm and superspace integration measure for 2D supergravity with four spinorial supercurrents, 0907.5264.
    • S. J. Gates and A. Morrison, A Derivation of an Off-Shell N = (2,2) Supergravity Chiral Projection Operator, 0901.4165.
  2. Dimensonal reduction in supersymmetry
    • For example, S. J. Gates and T. Hubsch, On dimensional extension of supersymmetry: From worldlines to worldsheets, 1104.0722, deals with reduction from 1+1 to 0+1 dimensions.
  3. Adinkras and combinatorics--- a few references:
    • Yan Zhang, The combinatorics of adinkras.
    • Yan Zhang, Adinkras for mathematicians, 1111.6055.
    • Greg Landweber, Bibliography on adinkras.
    • C. Doran, K. Iga, G. Landweber, and S. Mendez-Diez, Geometrization of N-extended 1-dimensional supersymmetry algebras, 1311.3736.
    • T. Hübsch and G.A. Katona, On the Construction and the Structure of Off-Shell Supermultiplet Quotients, Int. J. Mod. Phys. A27 (2012) 1250173, 1202.4342.
    • C.F. Doran, T. Hübsch, K.M. Iga and G.D. Landweber,  On General Off-Shell Representations of Worldline (1D) Supersymmetry, Symmetry 6 no. 1, (2014) 67–88, 1310.3258.
  4. Super-Riemann surfaces and physical applications
  5. The Haag-Łopuszański-Sohnius Theorem and its variants. This is the supersymmetric analogue of the better-known Coleman-Mandula Theorem.
  6. Mirror symmetry (2016-2017).  In the fall, we followed a somewhat ad hoc approach based on looking at a lot of examples (e.g., elliptic curves and the quintic Calabi-Yau).  In the spring, we followed the multi-author book published by AMS, Dirichlet Branes and Mirror Symmetry.  The preface and Chapter 1 can be downloaded from the AMS website; Chapter 2 is at arXiv:hep-th/0609042.  An electronic version of the whole book is available at

Topics and references for 2017-2018

The topic for fall 2017 is topological states of matter. In no particular order, here is a list of references:

  1. Emil Prodan and Hermann Schulz-Baldes, "Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics", arXiv:1510.08724.
  2. Daniel Freed and Greg Moore, Twisted equivariant matter, Ann. Henri Poincaré 14 (2013), no. 8, 1927–2023, arXiv:1208.5055.
  3. A. Kitaev, Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22–30 (2009). doi:10.1063/1.3149495, arXiv:0901.2686
  4. F.D.M. Haldane, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the "parity anomaly". Phys. Rev. Lett. 61, 2015–2018 (1988).
  5. C.L. Kane and E.J. Mele, Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005), arXiv:cond-mat/0411737
  6. C.L. Kane and E.J. Mele, Z2 Topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005), arXiv:cond-mat/0506581.
  7. C.L. Kane and E.J. Mele, Topological Mirror Superconductivity, Phys. Rev. Lett. 111, 056403 (2013), arXiv:1303.4144.
  8. Jean Bellissard, Noncommutative Geometry and the Quantum Hall Effect, Proceedings of the International Conference of Mathematicians (Zürich 94), Birkhäuser (1995).
  9. J. Bellissard, A. van Elst, H. Schulz-Baldes, The Non Commutative Geometry of the Quantum Hall Effect (longer version of #8 above), arXiv:cond-mat/9411052.
  10. David Tong: Lectures on the Quantum Hall Effect, Univ. of Cambridge, arXiv:1606.06687.
  11. Edward Witten, Three Lectures On Topological Phases Of Matter, arXiv:1510.07698.
  12. Ralph M. Kaufmann, Dan Li, and Birgit Wehefritz-Kaufmann, Notes on topological insulators, Rev. Math. Phys., 28(10), 1630003, 2016, arXiv:1501.02874.
  13. Anton Akhmerov, Jay Sau, et al., Topological condensed matter, an online course.

The topic for spring 2018 is generalized geometry and its applications to physics (especially supersymmetry and string theory). We will begin with the first reference listed, Hitchin's notes. Here is a short list of basic references:

  1. N. Hitchin, Lectures on Generalized Geometry, arXiv:1008.0973.
  2. M. Zabzine, Lectures on Generalized Complex Geometry and Supersymmetry, arXiv:hep-th/0605148.
  3. Dimitrios Tsimpis, Generalized geometry lectures on type II backgrounds, arXiv:1606.08674.
  4. N. Hitchin, Generalized Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), no. 3, 281–308, arXiv:math/0209099.
  5. M. Gualtieri, Generalized Kahler geometry, arXiv:1007.3485.
  6. G. Cavalcantri and M. Gualtieri, Generalized complex geometry and T-duality, arXiv:1106.1747.

Detailed schedule posted below.

Organizers: Ricardo Nochetto, Wujun Zhang
When: Wednesdays @ 5pm-6pm, starting the first week of February
Where: room TBA
Subtitle: PDE theory and numerical analysis

Fully nonlinear second order elliptic PDEs arise naturally from differential geometry, stochastic control theory, optimal transport and other fields in science and engineering. In this RIT, we will discuss the concept of viscosity solutions and regularity theory of these PDEs. Some possible topics include:

  • fully nonlinear elliptic equations and viscosity solutions
  • Alexandroff-Bakelman-Pucci estimates
  • Harnack inequality and Hölder regularity
  • Uniqueness of solutions
  • W2,p estimates
  • C1, α estimates
  • C2, α estimates

In contrast to an extensive PDE literature, the numerical approximation reduces to a few papers. We would like to discuss some criteria for designing convergent numerical methods and some tools developed recently which are useful to obtain rates of convergence. Some possible topics include:

  • criterion for convergence of numerical methods
  • discrete version of the Alexandroff-Bakelman-Pucci estimate
  • finite element method for linear elliptic equations in non-divergence form
  • numerical method for Monge-Ampere equations

Location: Math 3206
Day: Wednesday (with occasional talks Friday)
Time: 3:15pm
Tea: 2:45pm in 3201
Organizers: Giovanni Forni, Harry Tamvakis, Konstantina Trivisa

2011 - 2012 Colloquium Schedule

Sept 14

Wonderful compactifications of groups as moduli spaces of principal bundles
Michael Thaddeus (Columbia University),

Sept 28

An introduction to essential dimension
Patrick Brosnan(University of Maryland),

Oct 21

Rigidity of group actions, cohomology and compactness
David Fisher (Indiana University, Bloomington),

Oct 28

A Filtration of Open/Closed Topological Field Theory
Ezra Getzler (Northwestern University),

Nov 2

Rational billiards and the SL(2,R) action on moduli space
Alex Eskin (University of Chicago),

Nov 9

Why and how do we use wavelets to study turbulence?
Marie Farge(Directrice de Recherche CNRS)

Nov 16

Mixed volume computation and solving polynomial systems
Tien-Yien Li (Michigan State University),

Dec 2

Optimal and Practical Algebraic Solvers for Discretized PDEs - Aziz Lecture
Jinchao Xu (Pennsylvania State University),

Dec 7

Sastry G. Pantula(National Science Foundation)

Feb 8

On the rigidity of black holes - Douglis Lecture
Sergiu Klainerman(Princeton University )

Feb 17

Product formulas for positive measures and applications - February Fourier Talks
Peter Jones(Yale University),

Feb 22

Semismooth Newton Methods: Theory, Numerics and Applications - Aziz Lecture
Michael Hintermüller (Humboldt University, Berlin),

Feb 29

On the size of the Navier - Stokes singular set
Walter Craig (McMaster University),

Mar 14

De Giorgi methods applied to regularity issues in Fluid Mechanics
Alexis Vasseur (UT Austin )

Mar 30

Birkhoff Normal Form and a problem of Herman - Dynamics Conference
Hakan Eliasson (University of Paris-6 and IAS),

Apr 25

Lyapunov Functions: Towards an Aubry-Mather theory for homeomorphisms?
Albert Fathi (ENS-Lyon),

May 2

Contractions of Lie Groups and Representation Theory
Nigel Higson (Penn State University), cancelled

May 9

The Pfaffian-Grassmannian Derived Equivalence
Andrei Caldărăru (University of Wisconsin, Madison),

Organizers: Niranjan Ramachandran, Dio Margetis, and Leo Koralov
Wednesday @ 3:15pm, Tea 2:45pm - 3:15 pm in room 3201
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.

This area includes information on research done in the department, seminars and conferences hosted by the department, as well as access to electronic research resources.


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 ) -

    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 ) -

    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,
    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) -

    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) -

    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) -

    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 ) -

    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) -

    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) -

    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) - 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) -

    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) -

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

    Speaker: Richard Montgomery (UCSC) -

    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) -

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

    View Abstract

    Abstract: TBA
  • TBA

    Speaker: Alexander Vladimirsky (Cornell University) -

    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) -

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

    Speaker: Arnaud Debussche (ENS, Rennes, France) -

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