The Department of Mathematics at the College Park campus of the University of Maryland is pleased to announce the first Maryland Mathematics Institute (MMI), a week-long group of presentations and discussions that are designed to be stimulating and accessible to secondary school teachers.

### REGISTRATION INFORMATION:

Teachers interested in registering for the Institute should contact Professor Denny Gulick (contact information below) for a registration form.

Basic information:

• Dates: Monday, June 23 through Friday, June 27, 2008
• Times: 8:30am- 3:30pm, lunch to be provided by the University
• Location: Room 1311 in the Mathematics Building,
College Park campus of the University of Maryland
• Credits: 2 college credits from the University of Maryland
(enroll under MATH 498M)
• Cost to teachers enrolling in MATH 498M: $676 ($546 tuition + $55 application fee +$75 mandatory UMD fee)
• Lunch will be provided by the Department of Mathematics>
• Parking permits will be provided by the Department of Mathematics.
• Contact:
• Professor Denny Gulick ( 301 405 5157)

Day and Half-Day Interactive Presentations by University of Maryland Faculty:

• Dr. Michael Brin: Parallax, or How to Find the Distances to the Moon, Sun and Stars
• Dr. Michael Brin: Mathematics of the Search Engine Google <
• Dr. Daniel Chazan: From the History of Mathematics into the Classroom
• Dr. Denny Gulick: Famous Fractals, and How to Create Yours
• Dr. Frances Gulick: Playing with Geometer's Sketchpad
• Dr. Eric Slud: Experimental Statistics: from Monte Carlo Simulation to Bootstrap
• Dr. Larry Washington: Introduction to Cryptography, or How to Share Secrets

Also: Discussions on in-school topics of interest to teachers

Here are more details on the vision of the Mathematics Department of the University of Maryland, College Park, with respect to the Maryland Mathematics Institute: The Department envisions the MMI as an annual one-week, two-credit summer course featuring several College Park faculty. The aim is to provide high school mathematics teachers with interesting and enjoyable mathematics relevant to teaching high school students, and to communicate to the teachers the pleasure and relevance of mathematics. The topics entailed in the MMI will go beyond the standard courses preparatory for teaching high school mathematics.

The Department also aims to build communication between College Park faculty (primarily from the Mathematics Department but also from Mathematics Education) and high school teachers, and to provide high school mathematics teachers a setting to learn from each other and enhance their own community.

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

• #### Speaker: () -

When: Wed, September 13, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### 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 âtypicalâ 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.
• #### Speaker: (CMNS Dean's Office) -

When: Wed, September 27, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Vladimir Matveev (Friedrich-Schiller-UniversitÃ¤t Jena ) - http://users.minet.uni-jena.de/~matveev/

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

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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).
• #### Speaker: General Departmental Meeting () -

When: Wed, October 11, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Departmental Meeting () -

When: Wed, October 18, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Departmental Meeting () -

When: Wed, October 25, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### 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.
• #### Speaker: Pierre-Emmanuel Jabin (UMD) - http://www2.cscamm.umd.edu/~jabin/

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

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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
• #### Speaker: Simon Levin (Princeton ) -

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

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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 Darwinâs thinking, and has remained a theme explored by such key thinkers as Hutchinson (âThe paradox of the planktonâ), 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.
• #### Speaker: () -

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

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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.

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

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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.
• #### 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.

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

When: Fri, December 8, 2017 - 3:15pm
Where: Kirwan Hall 3206
• #### 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.
• #### 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.
• #### Speaker: Claude Le Bris () -

When: Wed, February 7, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### 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.
• #### 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.
• #### 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.
• #### 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.
• #### Speaker: Richard Schwartz (Brown University) - http://www.math.brown.edu/~res/

When: Wed, March 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Richard Montgomery (UCSC) - https://people.ucsc.edu/~rmont/

When: Wed, March 28, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Teaching forum () -

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

When: Wed, April 25, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: TBA Kirwan Lecture () -

When: Fri, April 27, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Lillian Pierce (Duke University/IAS) - https://services.math.duke.edu/~pierce/

When: Wed, May 2, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### 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