Seminars, Colloquia, and Conferences
Past Colloquia
The colloquium meets on Fridays at 4:00pm in
BromfieldPearson 101, unless otherwise indicated.
Spring 2018
January 19, 2018
Gaussian Curvature and Gyroscopes
Mark Levi (The Pennsylvania State University)
Abstract:
Some counterintuitive mechanical phenomena, such as the gyroscopic effect, turn out to be related to Gaussian curvature. This applies, for instance, to the Lagrange top, which is described in virtually every advanced text on classical mechanics,
but without reference to differential geometry.
I will describe this in more detail, for non–specialists, and will mention some interesting related things discovered in the last couple of decades
February 16, 2018
Title  TBD
February 23, 2018
Title  TBD
March 2, 2018
Title  TBD
March 9, 2018
Skew Flat Fibrations
Michael Harrison (Lehigh University)
Abstract:
Is it possible to cover 3dimensional space by a collection of lines, such that no
two lines intersect and no two lines are parallel? More precisely, does there exist
a fibration of R^3 by pairwise skew lines? We give some examples and provide a
complete classification of such objects, by exhibiting a deformation retract from the
space of skew fibrations of R^3 to the subspace of Hopf fibrations. As a corollary of
the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3.
We conclude with a discussion of skew fibrations in higher dimensions and some
surprising connections to the HurwitzRadon function and to vector fields on spheres.
March 16, 2018
Dual singularities in exceptional type nilpotent cones
Paul Levy (Lancaster University, UK)
Abstract:
It is wellknown that
nilpotent orbits in sl(n,C) correspond bijectively with the set of partitions of
n, such that the closure (partial) ordering on orbits is sent to the dominance
order on partitions. Taking dual partitions simply turns this poset upside down,
so in type A there is an orderreversing involution on the poset of nilpotent
orbits. More generally, if g is any simple Lie algebra over C then
LusztigSpaltenstein duality is an orderreversing bijection from the set of
special nilpotent orbits in g to the set of special nilpotent orbits in the
Langlands dual Lie algebra g^L. It was observed by Kraft and Procesi that the
duality in type A is manifested in the geometry of the nullcone. In particular,
if two orbits OO_1 < OO_2 are adjacent in the partial order then so are their
duals OO_1^t > OO_2^t, and the isolated singularity attached to the pair
(OO_1,OO_2) is dual to the singularity attached to (OO_2^t,OO_1^t): a Kleinian
singularity of type A_k is swapped with the minimal nilpotent orbit closure in
sl(k+1,C) (and viceversa). Subsequent work of KraftProcesi determined
singularities associated to such pairs in the remaining classical Lie algebras,
but did not specifically touch on duality for pairs of special orbits. In this
talk, I will explain some recent joint research with Fu, Juteau and Sommers on
singularities associated to pairs OO_1<OO_2 of (special) orbits in exceptional
Lie algebras. In particular, we (almost always) observe a generalized form of
duality for such singularities in any simple Lie algebra.
March 23, 2018
SPRING BREAK  no Colloquium
April 6, 2018
Developing a Coherent Approach to Multiplication in School Mathematics
Andrew Izsak (Tufts University)
Abstract:
Numerous national reports on the state of
education in school mathematics have highlighted the need to strengthen
instruction in topics related to multiplication. I will focus on one critical
aspect of this problem, the mathematical preparation of teachers. In particular,
I will report on an approach developed with colleagues at the University of
Georgia to teaching multiplication topics related to future middle and high
school teachers. The approach is based on reasoning from an explicit,
quantitative meaning for multiplication and mathematical drawings such as number
lines and strip diagrams with the goal of seeing common structure across topics
from multiplication to proportions using both whole numbers and fractions.
April 20, 2018
Uniform distribution, generalized polynomials and the theory of multiple recurrence
Vitaly Bergelson (Ohio State University)
Spring 2017
February 10, 2017
From Homogeneous Metric Spaces to Lie Groups
Sebastiano Nicolussi Golo (University of Jyväskylä & University of Trento)
February 24, 2017
Diophantine and tropical geometry
David ZureickBrown (Emory University)
March 3, 2017
Reflection Positivity:
Representation Theory meets Quantum Field Theory
Gestur Olafsson (LSU)
March 10, 2017
Diffusion of
Lorentz gas on scatterers with flat point
Hongkun Zhang (UMass Amherst)
March 17, 2017
Numerical difficulties
in the simulation of flow in deformable porous media
Carmen Rodrigo (University of Zaragoza, Spain)
March 31, 2017
Equidistribution
of Shapes of Number Fields of degree 3, 4, and 5
Piper Harron (University of Hawaii)
Abstract:
In her talk, Piper Harron will introduce the ideas that there are number fields,
that number fields have shapes, and that these shapes are everywhere you want them
to be. This result is joint work with Manjul Bhargava and uses his counting methods
which currently we only have for cubic, quartic, and quintic fields. She will sketch
the proof of this result and leave the rest as an exercise for the audience.
(Check your work by downloading her thesis!)
April 7, 2017
Fun with Finite Covers of 3Manifolds:
Connections between Topology, Geometry, and Arithmetic
Nathan Dunfield (University of Illinois at UrbanaChampagne)
Abstract:
From the revolutionary work of Thurston and Perelman, we know
that the topology of 3manifolds is deeply intertwined with their geometry.
In particular, hyperbolic geometry, the nonEuclidean geometry of
constant negative curvature, plays a central role. In turn, hyperbolic
geometry opens the door to applying tools from number theory,
specifically automorphic forms, to what might seem like purely
topological questions.
After a passing wave at the recent breakthrough results of Agol, I will
focus on exciting new questions about the geometric and arithmetic
meaning of torsion in the homology of finite covers of hyperbolic
3manifolds, motivated by the recent work of Bergeron, Venkatesh, Le,
and others. I will include some of my own results in this area that are
joint work with F. Calegari and J. Brock.
April 14, 2017
Crossing Matrices for Braids
Zbigniew Nitecki (Tufts University)
Abstract TBA:
Abstract: Given a geometric braid with N strands, one can codify the crossing information in an N by N matrix
whose ij entry is the algebraic number of crossings of strand i over strand j, that is, the number of
lefttoright crossings minus the number of righttoleft ones. This is the same for any two representatives
of the same braid (which is a homotopy class); this gives a matrixvalued “derivation” on the braid group
(at least Mo tells me that is what it is called). Mauricio Gutierrez and I, together with Pep Burillo and
Sava Krstic, published a paper about 15 years ago about these matrices, but one question was left open,
and has occupied Mo and me for the last too many years.
It is easy (using some general results on the braid group) to characterize which matrices occur as crossing
matrices for some braid, but the more interesting question is which ones occur for positive braids
(all crossings in the same direction) because then all the crossings appear (there is no cancellation).
The "obvious" answer to the positive realization question, adapting the answer for not necessarily positive braids,
is false, and we have been trying to find a characterization for crossing matrices of positive braids without
success for some time. We do, however, have an algorithmic answer, and a (limited) conjecture.
I plan to quickly introduce the basic notions of braids and the algebra of crossing matrices, the connection
between these and the ThurstonGarside normal form for braids, then try to explain what we know about the
characterization problem, as well as the algorithm we have which exhibits all possible realizations (if any exist)
of an appropriate matrix.
April 21, 2017
Inhibitionbased theta resonance in a hippocampal network
Horacio Rotstein (New Jersey Institute of Technology)
Abstract TBA:
Abstract: A crucial issue in the understanding of neuronal oscillations is to elucidate the microcircuits
that are the substrate to these rhythms in the different brain areas. This raises the question of whether
rhythmic activity results solely from the properties of the network connectivity (e.g., excitation and inhibition)
and topology or it involves the interplay of the latter with the intrinsic properties (e.g., ionic currents) of the
participating neurons. In this project we address this issue theoretically in the context of the hippocampal area
CA1 microcircuits, which include excitatory (PYR) and inhibitory (INT) cells. It has been observed that PYR exhibit
a preferred subthreshold frequency response to oscillatory inptus at (4  10 Hz) frequencies (resonance) 'in vitro.'
Contrary to expectation, these cells do not exhibit spiking resonance in response to 'in vivo' direct oscillatory
optogenetic activation, but, surprisingly, spiking resonance in PYR occurs when INT are activated. We combine
dynamical systems tools, biophysical modeling and numerical simulations to understand the underlying mechanisms of
these rather unexpected results. We show that the lowpass filter results form a combination of postinhibitory
rebound (the ability of a cell to spike in response to inhibition) and the intrinsic properties of PYR.
The bandpass filter requires additional timing mechanisms that prevent the occurrence of spikes at low frequencies.
We discuss various possible, conceptually different scenarios. These results and tools contribute to building a
general theoretical and conceptual framework for the understanding of preferred frequency responses to oscillatory
inputs in neuronal networks.
Fall 2016
September 16, 2016
Metamathematical framework for a new music; inspired by Algebraic Geometry
Bangere P. Purnaprajna (University of Kansas)
Abstract:
It is wellknown that one can obtain deep insights about algebraic varieties defined
over a field K by working in a more general setting where varieties are defined over
rings containing K. In particular, the behavior of a variety as it moves in a family is
of deep interest, and plays a vital role in the theory of moduli spaces. This viewpoint
has yielded many interesting results, a few of which are proved by the speaker and his
collaborators. Inspired by these results and by Grothendieck's writing on nilpotents
in algebraic geometry, we develop a meta geometric framework for a new music that
integrates elements of Indian and western classical music, Jazz and the Blues. This
is part of an ongoing work with David Balakrishnan, director of the Turtle Island
String Quartet. This talk will feature some music as well.
September 23, 2016
Tempered representations: the stellar picture
Pierre Clare (Dartmouth University)
Abstract:
HarishChandra's Plancherel formula for semisimple Lie groups is a deep result of
harmonic analysis that can be seen as a generalization of the theory of Fourier series
in the context of unitary representations. The classes of representations that occur in
the Plancherel measure of a given group form a topological space called the tempered dual
of that group.
The purpose of this talk is to show how the use of C*algebras allows to study the
tempered dual of a Lie group as a noncommutative space and casts a new light on
representationtheoretic problems. The main concepts will be illustrated on 'small'
concrete examples.
September 30, 2016
The social role of mathematical proofs
Kenny Easwaran (Texas A&M University)
Abstract:
Much of mathematics proceeds by means of proof, but what makes proofs different from
other forms of verification or communication? What is the role of proofs in spreading
mathematical knowledge? Does the success of a proof depend on trusting the author?
What would it take to conclusively defeat a proof?
The talk is at 4pm in Eaton 206 and will be aimed at a level suitable to students
without much background assumed in math or philosophy.
October 7, 2016
Student Presentations from Directed Reading Program
Ruth MeadowMcLeod, Ryan Kohl, and Zach Munro
October 14, 2016
Inverse Problems in Adaptive Optics
Ronny Ramlau (Johannes Kepler University Linz)
Abstract:
Currently there is a new generation of large astronomical telescope under construction,
e.g. the European Extremely Large Telescope (EELT) of the European Southern Observatory
(ESO) with a mirror diameter of 39 meters or the Thirty Meter Telescope (TMT), build by
a consortium headed by Caltech. The operation of those huge telescopes require new
mathematical methods in particular for the
Adaptive Optics systems of the telescopes.
The image quality of ground based astronomical telescopes suffers from
turbulences in the atmosphere. Adaptive Optics (AO) systems use wavefront
sensor measurements of incoming light from guide stars to determine an optimal
shape of deformable mirrors (DM) such that the image of the scientific object
is corrected after reflection on the DM. The solution of this task involves
several inverse problems: First, the incoming wavefronts have to be reconstructed
from wavefront sensor measurements. The next step involves the solution of the
Atmospheric Tomography problem, i.e., the reconstruction of the turbulence profile
in the atmosphere. Finally, the optimal shape of the mirrors has to be determined.
As the atmosphere changes frequently, these computations have to be done in real time.
In the talk we introduce mathematical models for the elements of different Adaptive Optics
system such as Single Conjugate Adaptive Optics (SCAO) or Multi Conjugate Adaptive Optics
(MCAO) and present fast reconstruction algorithms as well as related numerical results for
each of the subtasks that achieve the accuracy and speed required for the operation of ELTs.
October 21, 2016
Reconfiguring Chains with Discrete Moves: Flips and Pops
Dr. Perouz Taslakian [Université libre de Bruxelles (Brussels, Belgium) and ROI Research on Investment Corp. (Montreal, Canada)]
Abstract:
Understanding motion has long been a central theme in both the theoretical and
applied sciences. But even as our expanding knowledge of the mechanism in which
objects move has led to developments in an array of applications, many basic
questions remain unresolved.
In this talk, we will look into the mechanics of motion for polygonal chains
and explore the question of whether it is possible to move between two different
configurations of a given polygon using a predefined move. We frame our question
as a problem in discrete geometry, whereby the moves we consider are a discrete
sequence of steps. We will see that even when considering restricted moves applied
to simple objects such as polygons, reconfiguration questions remain challenging.
In particular, we will talk about Erdős flips, and a more restricted version of
such flips called pops. Given a polygonal chain that lies in the 2dimensional plane,
a pop reflects a vertex of this chain across the line through its two neighbouring
vertices such that the resulting polygon lies in the same plane. We will see that
using techniques from dynamical systems theory, we can show that for certain classes
of polygons, the neighbourhood of any configuration that can be reached by smooth
motion can also be reached by pops.
November 4, 2016
Economic inequality from statistical physics point of view
Victor Yakovenko (University of Maryland, Physics Dept.)
Abstract:
By analogy with the probability distribution of energy in statistical physics,
the probability distribution of money among the agents in a closed economic system
is expected to follow the exponential BoltzmannGibbs law, as a consequence of entropy
maximization. Analysis of empirical data shows that income distributions in the USA,
European Union, and other countries exhibit a welldefined twoclass structure.
The majority of the population (about 97%) belongs to the lower class characterized
by the exponential ("thermal") distribution. The upper class (about 3% of the population)
is characterized by the Pareto powerlaw ("superthermal") distribution, and its share of
the total income expands and contracts dramatically during booms and busts in financial
markets. Globally, data analysis of energy consumption per capita around the world shows
decreasing inequality in the last 30 years and convergence toward the exponential probability
distribution, in agreement with the maximal entropy principle. Similar results are found
for the global probability distribution of CO2 emissions per capita.
Read papers >
Recent coverage in Science magazine >
Spring 2016
March 11, 2016
Elliptic Curves, Triangles and Lfunctions
David Roe (University of Pittsburgh)
Abstract:
Given a positive integer n, is n the area of a right triangle with rational side lengths?
Called the congruent number problem, this question has a rich history culminating in a theorem
of Tunnell (1983) that relates it to elliptic curves of the form y^2 = x^3  n^2x. But the story
does not stop there, since a full resolution of the problem requires the Birch and SwinnertonDyer
conjecture, one of the million dollar Clay Math Prize problems.
I will describe the connection between the *rank* of an elliptic curve, the congruent number
problem and the Birch and SwinnertonDyer conjecture, giving many examples. If time permits,
I will also explore the rank of elliptic curves further by describing the search for curves
of high rank and some recent heuristics that suggest that the rank of an elliptic curve over*Q* may
be absolutely bounded.
March 18, 2016
The Theory of Chaos: Yesterday, Today and Tomorrow
Yakov Pesin (Pennsylvania State University)
Abstract:
The talk is a brief historical account of the development of the theory that
deals with the phenomenon widely known as "deterministic chaos"  the appearance
of irregular chaotic motions in purely deterministic dynamical systems on compact
phase spaces.
The hyperbolic theory of dynamical systems provides a mathematical foundation for
this paradigm and thus serves as a basis for the theory of chaos. The hyperbolic
behavior can be interpreted in various ways and the weakest one is associated with
dynamical systems with nonzero Lyapunov exponents.
I will describe various types of hyperbolicity, outline some examples of systems
with hyperbolic behavior and discuss the stillopen problem of whether chaotic
dynamical systems are generic. This genericity problem is closely related to two
other important problems in dynamics on whether systems with nonzero Lyapunov
exponents exist on any compact phase space and whether chaotic behavior can coexist
with a regular (nonchaotic) one in a robust way.
April 1, 2016
Markedlength spectrum rigidity for unfriendly spaces
David Constantine (Wesleyan University)
Abstract:
The markedlength spectrum rigidity problem is the following:
Given a geometric space, if we know the lengths of the shortest
curves representing each element of the fundamental group, can we
recover the full geometry of the space. This problem has been most
fruitfully studied in negative curvature, where closed geodesics are
dense. The answer is yes for closed, negatively curved Riemannian
surfaces, and for compact, negatively curved locally symmetric
spaces of all dimensions. In this talk I'll give a general overview
of this problem, and discuss a few recent results on extending MLS
rigidity away from the Riemannian setting, to metrics which have
some nonsmooth structure, and which even allow some zero curvature.
Portions of this work are joint with JeanFrancois Lafont.
April 8, 2016
Norbert Wiener Lecture
Noam Elkies (Harvard University)
April 15, 2016
Martin Guterman Lecture
John Urschel (MIT)
April 22, 2016
Structure of zero sets
of random waves on a manifold
Yaiza Canzani (Harvard University)
Abstract:
There are several questions about the zero set of Laplace eigenfunctions
that have proved to be extremely hard to deal with and remain unsolved.
Among these are the study of the size of the zero set, the study of the
number of connected components, and the study of the topology of such
components. A natural approach is to randomize the problem and ask the
same questions for the zero sets of random linear combinations of eigenfunctions.
In this talk I will present some recent results in this direction.
Fall 2015
September 18, 2015
Talks from the Directed Reading Program
Freddy Saia, Matt DiRe, Ryan HastingsEcho
(Tufts University)
Abstract:
Freddy Saia: "Continued Fractions and Transcendental Numbers" (mentor: Michael BenZvi)
We will begin by talking about continued fractions  what they are, some of their properties,
and the notation we will use to discuss them. We will then venture into seemingly unrelated territory,
presenting and proving Joseph Liouville's theorem on diophantine approximation. This theorem was used by
Liouville in the 1840s both to prove the existence of transcendental numbers (real numbers which are
not roots of any nonzero polynomials with rational coefficients) as well as to give specific examples
of such numbers, dubbed Liouville numbers (only a proper subset of the transcendentals, though still
uncountable). In this vein, we will use the properties of continued fractions we had previously
discussed to display a quick, neat construction of Liouville numbers.
Matt DiRe and Ryan HastingsEcho: "Gödel's Proof" (mentor: George Domat)
At the turn of the last century, mathematicians like Hilbert and Russell attempted to unify all
branches of mathematics within a single logical calculus. But, at the time, there were no tools
available to settle questions of inconsistency (contradictions derived within a system) or
incompleteness (existence of true, expressible statements with no formal proof) within a formal system.
In 1931, Kurt Gödel introduced a method, now know as Gödel numbering, which allowed him to translate
metamathematical statements into welldefined arithmetic relations expressible within the calculus.
Using Gödel numbering, he was able to explicitly express the statement “this statement is not expressible”
within the calculus, thus deriving a critical contradiction. The nuanced logic of this proof was
complex yet irrefutable, and it provided a definitive answer to the problem of inconsistency and
incompleteness.
September 25, 2015
An algorithm for phase retrieval with corrupted data
Paul Hand
(Rice University)
Abstract
Phase retrieval is the process of recovering a vector from phaseless
linear measurements. It is a challenging mathematical problem that
appears in Xray crystallography and other applications. The problem
is even more difficult in the presence of corrupted measurements, which
can occur because of occlusions, sensor failures, or sensor saturation.
In this talk we show that a wellknown semidefinite program can
successfully solve the phase retrieval problem under corrupted data.
Specifically, we show that under a Gaussian measurement model, any
signal can be recovered with high probability, provided there are
enough measurements and provided that at most a fixed fraction of
the measurements are arbitrarily corrupted. Of the standard classical
and recent methods to solve phase retrieval, this semidefinite program
is the only one that can succeed under arbitrarily corrupted data.
October 2, 2015
Understanding the Structure and Stability of Localized Patterns
Elizabeth Makrides
(Brown University)
Abstract:
Localized patterns, in which a spatially oscillatory pattern on a finite spatial range connects
to a homogeneous solution outside this range, have been observed in a wide variety of physical
contexts, from fluid flows to crime hot spots, and optical cavities to vegetative growth. The
bifurcation diagrams of such patterns often exhibit snaking behavior, in which a branch of
symmetric solutions winds back and forth between two limits of an appropriate parameter.
I will discuss analytical and numerical results on the existence, uniqueness, and stability
of both symmetric and asymmetric localized patterns. I will also discuss analytical results
on the appearance of localized solutions, including branch reorganization and drift speed,
upon perturbations breaking symmetries and/or variational structure, and provide numerical
illustrations of these results.
November 13, 2015
IwahoriHecke algebras and Schubert calculus
Matthew Douglass
(University of North Texas, National Science Foundation)
Abstract:
In this survey talk I will describe first the doublecoset construction of IwahoriHecke algebra
of a padic reductive group, and then the action of this algebra on the equivariant Ktheory of
flag varieties, with the goal of explaining a conjectural connection between KazhdanLusztig theory
(for affine Hecke algebras) and Schubert calculus (in equivariant Ktheory).
November 20, 2015
Beyond the triangle – Brownian motion, Ito calculus, and
FokkerPlanck equation: fractional generalizations
Sabir Umarov
(University of New Haven)
Abstract:
The triple relationship between Brownian motion, the Ito stochastic differential equation
driven by Brownian motion, and the associated FokkerPlanck equation is well known.
This talk will be devoted to fractional generalizations of this triple relationship
between a wide class of driving processes, corresponding SDEs, and associated deterministic
fractional order pseudodifferential equations with singular symbols.
December 11, 2015
PathIndependent Integrals in Equilibrium ElectroChemoMechanics
Jianmin Qu
(Tufts University)
Abstract:
Using Noether's first theorem, we constructed two types of pathindependent
integrals in equilibrium electrochemoelastic systems and proved their uniqueness.
These pathindependent integrals are the extensions of the classical J and Lintegrals
in elasticity. Similar to their elastic counterparts, the electrochemoelastic Jintegrals
and Lintegrals represent energy release when a crack or a cavity undergoes a translation
and rotation, respectively. Results of this study established a theoretical foundation
for energy conservation laws in equilibrium electrochemoelasticity. Such conservation
laws are useful in modeling various phenomena in electrochemoelastic systems.
In addition, the pathindependent integrals obtained here provide a theoretical tool
for understanding and a practical tool for numerical evaluation of singular fields
in electrochemoelasticity.
Spring 2015
January 16, 2015
Live Experiments, Theorem
Curation and Natural Math Understanding: The Future of Mathematics by Computer
Stephen Wolfram
(CEO of Wolfram Research)
Abstract
Over the past quarter century, Mathematica and WolframAlpha have greatly
increased the level of automation possible in doing mathematics. What does
the future hold for doing math by computer? What new directions and qualitative
changes can we expect? I will discuss the implications of some of my and my
company's current practical and theoretical projects on the future of research
and education in mathematics. I'll probably try some live, unscripted,
mathematical experiments. And I'll show examples of perhaps unexpected
ways in which mathematical skills are used in the world of technology.
January 23, 2015
Lagrangian Particle Methods for
Vortex Dynamics
Robert Krasny
(University of Michigan)
Abstract
This talk will describe how Lagrangian particle methods are
being used to study the dynamics of fluid vortices. These
methods track the flow map using adaptive particle
discretizations. The BiotSavart integral is used to recover the
velocity from the vorticity, and a tree code is used to reduce
the computation time from $O(N^2)$ to $O(N\log N)$, where $N$ is
the number of particles. I'll present computations of vortex
sheet motion in 2D flow with reference to KelvinHelmholtz
instability, the Moore singularity, spiral rollup, and chaotic
dynamics. Other examples include vortex rings in 3D flow, and
vortex dynamics on a rotating sphere.
January 30, 2015
Radon Transforms and Spherical Functions
Sigurdur Helgason
(Massachusetts Institute of Technology)
Abstract
The original problem is stated in the title of Radon's paper
from 1917: Determine a function on space X from its integrals over a
family of subsets of X. We shall discuss this problem form a general
viewpoint, leading up to integral transforms for homogeneous spaces in
duality, illustrated by several examples. We shall discuss several
instance of such problems in case X is a noncompact symmetric space.
February 13, 2015
Certified reduced basis methods and
reduced collocation methods
Yanlai Chen
(University of Massachusetts Dartmouth)
Abstract
Models of reduced computational complexity is indispensable in
scenarios where a large number of numerical solutions to a
parametrized partial differential equation are desired in a
fast/realtime fashion. These include simulationbased design,
parameter optimization, optimal control, multimodel/scale
analysis, uncertainty quantification etc. Thanks to an
offlineonline procedure and the recognition that the
parameterinduced solution manifolds can be well approximated by
finitedimensional spaces, reduced basis method (RBM) and
reduced collocation method (RCM) can improve efficiency by
several orders of magnitudes. The accuracy of the RB/RC solution
is maintained through a rigorous a posteriori error estimator
whose efficient development is critical.
In this talk, I will give a brief introduction of the RBM and
discuss recent and ongoing efforts to develop RCM, and the
accompanying parametric analytical preconditioning techniques
which are capable of improving the quality of the error
estimation uniformly on the parameter domain, and speeding up
the convergence of the reduced solution to the truth
approximation significantly. New ways of effectively bounding
the stability constants for the error estimation will also be
discussed. These results are critical in certifying the accuracy
of the reduced model and giving it a reliable predictive value.
February 27, 2015
Random groups in number theory and random integral matrices
Melanie Matchett Wood
(University of Wisconsin, Madison)
Abstract
There are certain finite abelian groups that arise from objects
in number theory that are quite mysterious and of great
interest, for example the class group arising from a finite
extension of the rational numbers, or the TateShafarevich group
of an elliptic curve y^2=x^3+ax+b (for some rational numbers a,b).
We discuss the question of what a class group of a random
extension, or the TateShafarevich group of a random elliptic
curve, looks like, and explain heuristics of several authors
including Cohen and Lenstra, and Delaunay, for how these random
groups behave. Finally we will relate the predictions of these
heuristics to phenomena that can be seen and proven about random
integral matrices.
March 6, 2015
Dynamical Chaos in Kepler Planetary Systems
Matthew Holman
(HarvardSmithsonian Center for Astrophysics)
Abstract
Of the Kepler planets that have been reported to date, a significant
fraction are in systems with multiple transiting planets. In some cases,
the signature of the gravitational interactions between planets in these
systems can be seen in the variations of their times of transit. By carefully
modeling the transit times, as well as investigating longterm stability, we
are able to measure or constrain the masses and orbits of the transiting bodies
in some of these systems, verifying that they are indeed planets. Although this
approach is particularly effective for closely packed and nearresonant systems,
it has also been applied to a broad range of systems. These include circumbinary
planets, as well as systems with additional nontransiting planets. Some of the
Kepler planetary systems exhibit evidence of dynamical chaos on remarkably short
time scales, yet these systems are likely to be longlived. I will highlight the
theoretical advances in our understanding of dynamical chaos and stability that
have been prompted by the Kepler planetary systems.
April 3, 2015
A differentialgeometric
construction of differential Ktheory
Scott Wilson
(Queen's College, City University of New York)
Abstract
Cohomology theories are among the fundamental objects of study in topology, having a
wealth of interesting structures and useful applications. Recent research has focused
on certain refinements of cohomology theories that produce nonhomotopy invariants.
These refinements are known as differential cohomology theories, since they often
incorporate the data of differential forms. In this talk I'll describe a new construction
of one such theory (differential Ktheory) that uses only familiar objects from topology
and geometry. As time permits, I will indicate some applications and connections with
other areas of mathematics.
April 10, 2015
How finite
are infinite groups?
Stefan Witzel
Abstract
There are various ways to measure how "finite" an infinite group is. For example
one might say that a group is "more finite" if it admits a finite set of generators
than if it doesn't. I will talk about a variety of such properties coming from
topology. I will then give an overview of what is known about about the finiteness
properties of several groups and how those can be proven.
April 17, 2015
Cascadic Multigrid
for Eigenvalue Problems and Its Application in Graph Problems
Xiaozhe Hu
(Tufts University)
Abstract
In this work, we develop a cascadic multigrid method for the elliptic
eigenvalue problems and show its optimality under certain assumptions.
We also develop an algebraic variant for the fast computation of the
eigenvalue problems of a graph Laplacian and explore the applicability
of such an eigensolver to the graph related problems. Numerical tests
for practical graphs are presented to show the efficiency of the proposed
cascadic multigrid method. This is a joint work with J. Urschel, J. Xu,
and L. Zikatanov.
April 24, 2015 at 3:00pm
Entropy for smooth systems
Todd Fisher
(Brigham Young University)
Abstract
Dynamical systems studies the longterm behavior of systems that evolve in time.
It is well known that given an initial state the future behavior of a system is
unpredictable, even impossible to describe in many cases. The entropy of a system
is a number that quantifies the complexity of the system. In studying entropy,
the nicest classes of smooth systems are ones that do not undergo bifurcations for
small perturbations.
In this case, the entropy remains constant under perturbation. Outside of the class of systems,
a perturbation of the original system may undergo bifurcations. However, this is a local phenomenon,
and it is unclear when and how the local changes in the system lead to global changes in the
complexity of the system. We will state recent results describing how the entropy (complexity)
of the system may change under perturbation for certain classes of systems.
Fall 2014
September 15, 2014
A Weighted Wavelet Method for Region of Interest Tomography
Esther Kann
University of Linz, Industrial Mathematics Institute
September 19, 2014
How well can you see the slope of a digital line
(and other applications of the "tapering trick")?
James Propp
University of Massachusetts, Lowell
Abstract
In many situations, we want to estimate some asymptotic quantity
using data taken from a finite window. How can we best compensate for
the error introduced by the finiteness of the window?
There is a simple general method for doing this that often gives markedly
improved estimates, even though the method requires no information about
the relationship between windowsize and error. The method is called
"tapering" in the signalprocessing literature and "smoothing" in the
numbertheory literature, but outside of these two disciplines it does not
seem to have gotten the attention it deserves.
I will discuss applications of tapering related to such topics as computational
geometry, almostperiodic functions, latticepoint enumeration, number theory,
quasicrystals, and derandomized Markov chains. No special background in any of
these fields (or indeed much of anything beyond calculus) is required, though
a rudimentary knowledge of Fourier analysis will be helpful for those who want
to understand when and why tapering works.
September 26, 2014
Modeling of highly deformable materials
Luis Dorfmann
Tufts University
Abstract
The seminar starts by reviewing experimental data to illustrate the large
deformation stressstrain response of nonlinear elastic materials. This is
followed by a summary of the main ingredients of the nonlinear theory of
elasticity and of suitable strainenergy functions to describe the isotropic
and anisotropic responses of highly deformable materials. The second part of
the seminar focuses on the coupling of mechanical and magnetic effects and on
the development of constitutive equations for magnetoelastic materials. These
smart materials typically consist of an elastomeric matrix and a distribution
of nanoscale ferromagnetic particles and have the capability to change their
mechanical properties by the application of a magnetic field. We summarize the
relevant equations and propose a coupled freeenergy formulation, which depends
on the deformation gradient and on the magnetic induction. Finally, we discuss
how constitutive equations are specialized to isotropic incompressible magnetosensitive
elastomers in either Lagrangian or Eulerian forms.
October 3, 2014
From molecular dynamics to kinetic theory and hydrodynamics
Laure SaintRaymond
École Normale Supérieure, Paris
Abstract
A gas can be considered either as a large system of microscopic
interacting particles, or as a continuous medium governed by
fluid equations. A natural question is therefore to understand
whether both kinds of models give consistent predictions of the
dynamics.
In this lecture, we will focus on the validity of the fluid
approximation in the particular case of rarefied gases, using
kinetic theory as an intermediate level of description as
suggested by Hilbert in his sixth problem. We will present
landmark partial results, both on the low density limit and on
the NavierStokes limit of the Boltzmann equation, giving an
hint of the mathematical tools used to establish these
convergences, and discussing the challenging open questions.
October 17, 2014
Representations and subgroup structure of simple groups
Pham Tiep
University of Arizona
Abstract
What can one say about maximal subgroups, or, more generally, subgroup structure
of simple, finite or algebraic, groups? In this talk we will discuss how group
representation theory helps us study this classical problem. We will also describe
applications of these results to various problems, particularly in number theory
and algebraic geometry.
October 24, 2014
Statistical properties of deterministic systems by elementary means
Boris Hasselblatt
Tufts University
Abstract
The MaxwellBoltzmann ergodic hypothesis aimed to lay a foundation under
statistical mechanics, which is at a microscopic scale a deterministic system.
Similar complexity was discovered by Poincaré in celestial mechanics and by Hadamard
in the motion of a free particle in a negatively curved space. We start with a guided
tour of the history of the subject from various perspectives and then discuss the
central mechanism that produces pseudorandom behavior in these deterministic systems,
the Hopf argument. It has been known to extend well beyond the scope of its initial
application in 1939, and we show that it also leads to much stronger conclusions:
Not only do time averages of observables coincide with space averages (which was the
purpose for making the ergodic hypothesis), but any finite number of observables will
become decorrelated with time. That is, the Hopf argument does not only yield ergodicity
but mixing, and often mixing of all orders.
October 31, 2014
A New and Direct Proof of the Central Limit Theorem
Patricia Garmirian
Tufts University
Abstract
The Central Limit Theorem (CLT) is one of the most fundamental theorems in probability theory.
The CLT states that a sequence of appropriately scaled sums of i.i.d.
random variables converges weakly to the standard normal
distribution. Although mathematicians had worked on the CLT as
early as the 1600s, William Feller gave a proof of the CLT in
1935 by employing L\'evy's continuity theorem.
L\'evy's continuity theorem, a nontrivial result, establishes the equivalence of weak convergence for a
sequence of random variables and the convergence of the characteristic functions for those random variables.
In this talk, I will present the main ideas of our direct proof of the CLT which does not employ L\'evy's
continuity theorem. In our proof, we transform a random variable into an i.i.d. sequence on [0,1] and then
expand this sequence with respect to the Haar wavelet basis.
The theorem of Skorokhod can be applied to the CLT to establish the existence of a sequence of random
variables converging almost surely to the standard normal distribution. In this talk, I will also discuss
our present research in which we apply Skorokhod's theorem to a sequence of appropriately scaled sums of
i.i.d. random variables.
November 7, 2014
Hydrokinetic approach to complex flows:
the legacy of P.L. Bhatnagar
Sauro Succi
Istituto per le Applicazioni del Calcolo 'Mauro Picone'
Abstract
Kinetic theory was originally devised by Ludwig
Boltzmann to deal with rarefied gas dynamics.
However, in the last decades it has become
increasingly apparent that kinetic theory provides a
very powerful and general mathematical framework for
studying the dynamic evolution of a broad class of
complex systems at large. Instrumental to this
success, is the development of model Boltzmann
equations capable of relinquishing most mathematical
complexities without surrendering the essential
physics. In this talk we shall discuss the special
role played by lattice versions of the BhatnagarGrossKrook
model equation to model a variety of complex flows,
ranging from fluid turbulence to quarkgluon
plasmas.
November 14, 2014
Nonlinear stability of coherent structures via pointwise estimates
Margaret Beck
Abstract
Coherent structures, for example traveling waves and periodic patterns, play a key role in determining
the behavior of certain types of PDEs, such as reaction diffusion equations and viscous conservation laws.
In particular, if they are stable, then they attract nearby initial data and thus qualitatively govern the
local dynamics for large times. Determining the stability of coherent structures is often complicated by
the presence of continuous spectrum for the associated linearized operator, as well as by details of the
nonlinear terms in the PDE. In this talk, I will explain such difficulties in the context of patterns known
as defects, and explain how they can be overcome using socalled pointwise estimates for the associated
Green's function.
November 21, 2014
The dynamics of the normalized Ricci flow on some homogeneous spaces
Andreas Arvanitoyeorgos
Tufts University
December 5, 2014
Multiscale modeling using Lagrangian
particlebased methods
Wenxiao Pan
Northwestern National Laboratory
Abstract
Lagrangian particlebased methods have advantages for modeling
physical phenomena involving multiphase flows, flows with free
surfaces, advectiondominated flows, complex fluids,
largedeformation of materials and soft matters. In this talk, I
will discuss several particlebased methods including smoothed
particle hydrodynamics, smoothed dissipative particle dynamics
and dissipative particle dynamics. Their various applications in
macroscale and mesoscale multiphysical modeling will be
demonstrated.
December 12, 2014
Anderson 208
Abelian Networks: From Local to Global
Lionel Levine
Cornell University
Abstract
An abelian network is a collection of automata that live at the vertices of
a graph and communicate via the edges. It produces the same output no matter
in what order the automata process their inputs. Such a network can be viewed
as an interacting particle system or as a model of asynchronous computation.
This talk will survey the foundations of the subject, focusing on localtoglobal
principles, the halting problem, and groups and monoids associated to an abelian
network. Based on joint work with Ben Bond (Stanford) and James Propp (Tufts).
Spring 2014
Fall 2013
Spring 2013
Fall 2012
Spring 2012
Friday, Feb 10 
Dirk Schleicher
Jacobs University 
The dynamics of Newton's method as an efficient root finder 
Friday, March 9
2:003:00pm 
Sergio Fenley
Princeton 
TBA 
Friday, March 9 
Margarida Melo
Universidade de Coimbra 
TBA 
Friday, March 16 
Michael Burr
Fordham University 
TBA 
March 2730
(special times) 
Jordan S. Ellenberg
University of Wisconsin 
Norbert Wiener Lectures:
How to Count 
Friday, March 30 
Jon Hall
Michigan State University 
TBA 
Friday, April 6 
Sarah Koch
Harvard 
TBA 
Thursday, April 12 
Frank Morgan
Williams College 
Guterman Lecture:
Soap Bubbles and Mathematics 
Friday, April 13 
Craig Sutton
Dartmouth College 
TBA 
Friday, April 20 
Misha Kazhdan
Johns Hopkins 
Can Mean Curvature Flow Be Made NonSingular? 
Fall 2011
Spring 2011
April 22 
Nathan Dunfield
University of Illinois at
UrbanaChampaign 
Surfaces in finite covers of 3manifolds: the
Virtual Haken Conjecture 
April 8 
Alexander A. Ivanov
Imperial College 
The Monster Group and Majorana Involutions 
April 1 
Diane Prost O'Leary
University of Maryland 
Norbert Wiener Lecture
Undergraduate Seminar: Where Am I?
Position from incomplete distance
information, from Gauss's geodesy problems to
protein structures 
March 31 
Diane Prost O'Leary
University of Maryland 
Norbert Wiener Lecture
Seminar: Uncertainty Quantification for
Illposed Problems 
March 30 
Diane Prost O'Leary
University of Maryland 
Norbert Wiener Lecture
Mathematics in Words and Images
The role mathematics plays in searching the
web and in restoring blurred images. 
March 18 
Keith Burns
Northwestern University 
Ergodicity of the Weil Petersson geodesic flow 
March 15 
John Meier
Lafayette College 
The Martin Guterman Lecture
Euler, Graphs, and Surfaces 
February 25 
Ryan Kinser
University of Connecticut 
Dimension inequalities for subspace arrangements 
Fall 2010
December 10 
Enrique Pujals
Tufts University
Instituto Nacional de Matemática Pura e Aplicada 
Robust and Generic Dynamics: A phenomenon/mechanism correspondence 
November 12 
Csaba David T'oth
University of Calgary 
Enumeration of geometric graphs 
October 29 
Anish Ghosh
University of East Anglia 
Diophantine approximation on homogeneous varieties 
October 22 
Jens Christensen
Norbert Wiener Center for Harmonic Analysis and
Applications University of Maryland 
Smoothness criteria for sampling in reproducing kernel Banach spaces 
October 15 
Alberto Arabia 
The Weil conjecture and padic cohomology 
October 8 
Martin Krupa Radboud
Universiteit Nijmegen 
TBA 
Spring 2010
May 6 
Alexander Elgart
Virginia Tech 
Hamiltonianbased quantum computing for lowrank matrices 
April 30 
Liam Clegg, Victor Minden, and Daniel Brady
Tufts University 
From Kills to Kilometers:
Using Centrographic Techniques and Rational
Choice Theory for Geographical Pro filing of
Serial Killers 
April 23 
Christian Benes
Brooklyn College of the City University
of New York 
The SchrammLoewner Evolution 
April 16 
Adam Piggott
Bucknell University 
On the Derived Series of Coxeter Groups 
April 9 
Lloyd Nicholas Trefethen
Oxford University 
Four bugs on a rectangle (and the biggest
numbers you've ever seen) 
April 2 
Predrag Cvitanović
Department of Physics
Georgia Institute of Technology 
Geometry of boundary shear turbulence: a stroll
through 61,506 dimensions 
March 12 
Matt Knepley
University of Chicago 
Implementation for scientific computing: Finite
element methods and fast multipole methods' 
March 5 
Karen Braman
South Dakota School of Mines and Technology 
Thirdorder tensors as linear operators on a
space of matrices 
February 26 
Frantisek Matus
Institute of Information Theory
and Automation, Academy of
Sciences of the Czech Republic 
Matroids and entropy 
February 19 
Sergio Fenley
Florida State University
Princeton University 
Quasigeodesic pseudoAnosov flows 
February 12 
Bei Zeng
Institute for Quantum Computing, Waterloo 
Quantum Error Correction beyond Stabilizer Codes 
Fall 2009
December 4 
Sabir Umarov
Tufts University 
Stochastic
differential equations driven by a timechanged
Levy process and their associated fractional
differential equations 
December 3 
Raluca Felea
(Rochester Institute of Technology) 
Composition of Fourier integral operators with
fold and cusp singularities 
November 20 
Michele Benzi
(Emory University) 
Matrix functions in quantum chemistry and network analysis 
November 13 
Vidhu S. Prasad
University of Massachusetts, Lowell 
Hereditary tiles of the integers, and ergodic
transformations preserving an infinite measure 
November 6 
Souleymane Konate 
An exact inversion algorithm for the distorted
circle and line trajectory 
October 30 
Renato Feres
Washington University and University of Massachusetts, Amherst 
Random Billiards 
October 16 
Kevin Wortman
(University of Utah) 
Trees and groups 
October 9 
William Kantor
(University of Oregon) 
Presentations of simple groups 
October 2 
Mark Meerschaert
(Michigan State) 
Continuoustime random walks, fractional
calculus, and applications 
October 1 
Sauro Succi
Istituto Applicazioni CalcoloCNR Rome 
Large scale Lattice Boltzmann simulations of
cardiovascular flows on GPU hardware 
September 18 
Eriko Hironaka
(Florida State University) 
Lehmer's problem and dynamics on surfaces 
September 15 
Ronny Ramlau
Industrial Mathematics Institute
Johannes Kepler Universität
Linz, Austria 
Tikhonov regularization with sparsity
constraints  Regularization properties,
convergence rates and optimization 
September 11 
Stephen Wiggins
(University of Bristol) 
Mixing: From ergodic theory to applications, and back
again 
September 4 
Constantino Tsallis
CBPF, Rio de Janeiro, Brazil 
Entropy, Gaussians and Lyapunov exponents: what
can we do when the standard concepts come up
short? 
August 21 
Esther Klann
Johann Radon Institute for Computational and
Applied Mathematics (RICAM) 
A MumfordShah Like Approach For Tomography Data:
Reconstruction And Regularization 
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