Difference between revisions of "Colloquia"

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__NOTOC__
 
 
 
= Mathematics Colloquium =
 
= Mathematics Colloquium =
  
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
 
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.
  
<!-- ==[[Tentative Colloquia|Tentative schedule for next semester]] == -->
+
The calendar for spring 2019 can be found [[Colloquia/Spring2019|here]].
 +
 
 +
== Fall 2018 ==
  
==Fall 2017==
 
  
 
{| cellpadding="8"
 
{| cellpadding="8"
!align="left" | Date    
+
!align="left" | date    
!align="left" | Speaker
+
!align="left" | speaker
!align="left" | Title
+
!align="left" | title
!align="left" | Host(s)
+
!align="left" | host(s)
 
|-
 
|-
|September 8
+
|Sep 12    '''Room 911'''
| [https://sites.google.com/a/wisc.edu/theresa-c-anderson/home/ Tess Anderson] (Madison)
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#September 8: Tess Anderson (Madison) |  A Spherical Maximal Function along the Primes ]]
+
|[[#Sep 12: Gunther Uhlmann (Univ. of Washington)|  Harry Potter's Cloak via Transformation Optics ]]
| Tonghai Yang
+
| Li
 
|
 
|
 
|-
 
|-
|September 15
+
|Sep 14    '''Room 911'''
|
+
| [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series
|[[#|   ]]
+
|[[#Sep 14: Gunther Uhlmann (Univ. of Washington) | Journey to the Center of the Earth  ]]
|
+
| Li
|
+
 
|
 
|
 
|-
 
|-
|September 22, '''9th floor'''
+
|Sep 21    '''Room 911'''
| Jaeyoung Byeon (KAIST)
+
| [http://stuart.caltech.edu/  Andrew Stuart] (Caltech) LAA lecture
|[[#September 22: Jaeyoung Byeon (KAIST) |  Patterns formation for elliptic systems with large interaction forces ]]
+
|[[#Sep 21: Andrew Stuart (Caltech) |  The Legacy of Rudolph Kalman ]]
| Paul Rabinowitz & Chanwoo Kim
+
| Jin
 
|
 
|
|
 
|
 
|-
 
|October 6,  '''9th floor'''
 
| [http://www3.nd.edu/~jhauenst/ Jonathan Hauenstein] (Notre Dame)
 
|[[#October 6: Jonathan Hauenstein (Notre Dame) |  Real solutions of polynomial equations ]]
 
| Nigel Boston
 
|
 
 
|-
 
|-
|October 13, '''9th floor'''
+
|Sep 28
| [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
+
| [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU)
|[[#October 13: Tomoko Kitagawa (Berkeley) | A Global History of Mathematics from 1650 to 2017 ]]
+
|[[#Sep 28: Gautam Iyer (CMU)| Stirring and Mixing ]]
| Max
+
| Thiffeault
 
|
 
|
 
|-
 
|-
|October 20
+
|Oct 5
| [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)  
+
| [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State)
|[[#October 13: Pierre Germain (Courant, NYU) |  Stability of the Couette flow in the Euler and Navier-Stokes equations ]]
+
|[[#Oct 5: Eyal Subag (Penn State)|  Symmetries of the hydrogen atom and algebraic families  ]]
| Minh-Binh Tran
+
| Gurevich
 
|
 
|
 
|-
 
|-
|October 27
+
|Oct 12
|Stefanie Petermichl (Toulouse)
+
| [https://www.math.wisc.edu/~andreic/ Andrei Caldararu] (Madison)
|[[#October 27: Stefanie Petermichl (Toulouse) | Higher order Journé commutators ]]
+
|[[#Oct 12: Andrei Caldararu (Madison) | Mirror symmetry and derived categories ]]
| Betsy Stovall, Andreas Seeger
+
| ...
 
|
 
|
 
|-
 
|-
|We, November 1,
+
|Oct 19
|[http://pages.iu.edu/~shaoguo/  Shaoming Guo] (Indiana)
+
| [https://teitelbaum.math.uconn.edu/# Jeremy Teitelbaum] (U Connecticut)
|[[#November 1: Shaoming Guo (Indiana)|  Parsell-Vinogradov systems in higher dimensions ]]
+
|[[#Oct 19:   Jeremy Teitelbaum (U Connecticut)|  Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist ]]
|Andreas Seeger
+
| Boston
|
+
|
+
|
+
|
+
 
|
 
|
 
|-
 
|-
|November 17
+
|Oct 26
| [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)
+
| [http://math.arizona.edu/~ulmer/index.html Douglas Ulmer] (Arizona)
|[[#November 17:Yevgeny Liokumovich (MIT)|  Recent progress in Min-Max Theory  ]]
+
|[[#Oct 26: Douglas Ulmer (Arizona) | Rational numbers, rational functions, and rational points ]]
|Sean Paul
+
| Yang
|-
+
|November 21, '''9th floor'''
+
| [https://web.stanford.edu/~mkemeny/homepage.html Michael Kemeny] (Stanford)
+
|[[#November 21:Michael Kemeny (Stanford)| The equations defining curves and moduli spaces  ]]
+
|Jordan Ellenberg
+
 
|
 
|
 
|-
 
|-
|November 24
+
|Nov 2
|'''Thanksgiving break'''
+
| Reserved for job talk
|
+
|[[# TBA|  TBA  ]]
 +
| hosting faculty
 
|
 
|
 
|-
 
|-
|November 27,
+
|Nov 9
| [http://www.math.harvard.edu/~tcollins/homepage.html  Tristan Collins] (Harvard)
+
| Reserved for job talk
|[[#November 27:Tristan Collins (Harvard)The J-equation and stability ]]
+
|[[# TBATBA ]]
|Sean Paul
+
| hosting faculty
|
+
 
|
 
|
 
|-
 
|-
|December 5 (Tuesday)
+
|Nov 16
| [http://web.sas.upenn.edu/rhynd/  Ryan Hynd] (U Penn)
+
| Reserved for job talk
|[[#December 5: Ryan Hynd (U Penn)Adhesion dynamics and the sticky particle system]]
+
|[[# TBATBA  ]]
|Sigurd Angenent
+
| hosting faculty
 
|
 
|
 
|-
 
|-
|December 8 (Friday)
+
|Nov 30
| [https://cims.nyu.edu/~chennan/  Nan Chen] (Courant, NYU)
+
| Reserved for job talk
|[[#December 8: Nan Chen (Courant, NYU)A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]
+
|[[# TBATBA ]]
|Leslie Smith
+
| hosting faculty
|
+
 
|
 
|
 
|-
 
|-
|December 11 (Monday)
+
|Dec 7
| [https://people.math.ethz.ch/~mooneyc/  Connor Mooney] (ETH Zurich)
+
| Reserved for job talk
|[[#December 11: Connor Mooney (ETH Zurich)Regularity vs. Singularity for Elliptic and Parabolic Systems]]
+
|[[# TBATBA  ]]
|Sigurd Angenent
+
| hosting faculty
 
|
 
|
|-
 
|December 13 (Wednesday)
 
| [http://math.mit.edu/~blwilson/ Bobby Wilson] (MIT)
 
|[[#December 13: Bobby Wilson (MIT) | Projections in Banach Spaces and Harmonic Analysis ]]
 
|Andreas Seeger
 
|
 
|-
 
|December 15 (Friday)
 
| [http://roy.lederman.name/ Roy Lederman] (Princeton)
 
|[[#December 15: Roy Lederman (Princeton) | Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM) ]]
 
|Leslie Smith
 
|
 
|-
 
|December 18 (Monday)
 
| [https://web.stanford.edu/~jchw/ Jenny Wilson] (Stanford)
 
|[[#December 18: Jenny Wilson (Stanford)|  Stability in the homology of configuration spaces]]
 
|Jordan Ellenberg
 
|
 
|-
 
|December 19 (Tuesday)
 
| [https://web.stanford.edu/~amwright/  Alex Wright] (Stanford)
 
|[[#December 19: Alex Wright (Stanford)|  Dynamics, geometry, and the moduli space of Riemann surfaces]]
 
|Jordan Ellenberg
 
 
|}
 
|}
  
== Fall Abstracts ==
+
== Abstracts ==
=== September 8: Tess Anderson (Madison) ===
+
Title: A Spherical Maximal Function along the Primes
+
  
Abstract: Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example.  In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to.  We further quantify this with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory.  This is joint work with Cook, Hughes, and Kumchev.
+
=== Sep 12: Gunther Uhlmann (Univ. of Washington) ===
 +
Harry Potter's Cloak via Transformation Optics
  
 +
Can we make objects invisible? This has been a subject of human
 +
fascination for millennia in Greek mythology, movies, science fiction,
 +
etc. including the legend of Perseus versus Medusa and the more recent
 +
Star Trek and Harry Potter. In the last fifteen years or so there have been
 +
several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion
 +
one of them, the so-called "traansformation optics"
 +
in a non-technical fashion n the so-called that has received the most attention in the
 +
scientific literature.
  
=== September 22: Jaeyoung Byeon (KAIST) ===
+
=== Sep 14: Gunther Uhlmann (Univ. of Washington) ===
Title: Patterns formation for elliptic systems with large interaction forces
+
Journey to the Center of the Earth
  
Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions.  The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.
+
We will consider the inverse problem of determining the sound
 +
speed or index of refraction of a medium by measuring the travel times of
 +
waves going through the medium. This problem arises in global seismology
 +
in an attempt to determine the inner structure of the Earth by measuring
 +
travel times of earthquakes. It has also several applications in optics
 +
and medical imaging among others.
  
===October 6: Jonathan Hauenstein (Notre Dame) ===
+
The problem can be recast as a geometric problem: Can one determine the
Title: Real solutions of polynomial equations
+
Riemannian metric of a Riemannian manifold with boundary by measuring
 +
the distance function between boundary points? This is the boundary
 +
rigidity problem. We will also consider the problem of determining
 +
the metric from the scattering relation, the so-called lens rigidity
 +
problem. The linearization of these problems involve the integration
 +
of a tensor along geodesics, similar to the X-ray transform.
  
Abstract: Systems of nonlinear polynomial equations arise frequently in applications with the set of real solutions typically corresponding to physically meaningful solutions.  Efficient algorithms for computing real solutions are designed by exploiting structure arising from the application. This talk will highlight some of these algorithms for various applications such as solving steady-state problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steady-state solutions of the Kuramoto model.
+
We will also describe some recent results, join with Plamen Stefanov
 +
and Andras Vasy, on the partial data case, where you are making
 +
measurements on a subset of the boundary. No previous knowledge of
 +
Riemannian geometry will be assumed.
  
===October 13: Tomoko Kitagawa (Berkeley) ===
+
=== Sep 21: Andrew Stuart (Caltech) ===
Title: A Global History of Mathematics from 1650 to 2017
+
  
Abstract: This is a talk on the global history of mathematics. We will first focus on France by revisiting some of the conversations between Blaise Pascal (1623–1662) and Pierre de Fermat (1607–1665). These two “mathematicians” discussed ways of calculating the possibility of winning a gamble and exchanged their opinions on geometry. However, what about the rest of the world? We will embark on a long oceanic voyage to get to East Asia and uncover the unexpected consequences of blending foreign mathematical knowledge into domestic intelligence, which was occurring concurrently in Beijing and Kyoto. How did mathematicians and scientists contribute to the expansion of knowledge? What lessons do we learn from their experiences?
+
The Legacy of Rudolph Kalman
  
 +
In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.
  
 +
=== Sep 28: Gautam Iyer (CMU) ===
  
===October 20: Pierre Germain (Courant, NYU) ===
+
Stirring and Mixing
Title: Stability of the Couette flow in the Euler and Navier-Stokes equations
+
  
Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and Navier-Stokes. The Couette flow is the simplest nontrivial stationary flow, and the first one for which this question can be fully answered. The answer involves the mathematical understanding of important physical phenomena such as inviscid damping and enhanced dissipation. I will present recent results in dimension 2 (Bedrossian-Masmoudi) and dimension 3 (Bedrossian-Germain-Masmoudi).
+
Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical
 +
aspects of mixing that arise in the context of fluid dynamics:
  
===October 27: Stefanie Petermichl (Toulouse)===
+
1. How efficiently can stirring "mix"?
Title: Higher order Journé commutators
+
  
Abstract: We consider questions that stem from operator theory via Hankel and
+
2. What is the interaction between diffusion and mixing.
Toeplitz forms and target (weak) factorisation of Hardy spaces. In
+
more basic terms, let us consider a function on the unit circle in its
+
Fourier representation. Let P_+ denote the projection onto
+
non-negative and P_- onto negative frequencies. Let b denote
+
multiplication by the symbol function b. It is a classical theorem by
+
Nehari that the composed operator P_+ b P_- is bounded on L^2 if and
+
only if b is in an appropriate space of functions of bounded mean
+
oscillation. The necessity makes use of a classical factorisation
+
theorem of complex function theory on the disk. This type of question
+
can be reformulated in terms of commutators [b,H]=bH-Hb with the
+
Hilbert transform H=P_+ - P_- . Whenever factorisation is absent, such
+
as in the real variable setting, in the multi-parameter setting or
+
other, these classifications can be very difficult.
+
  
Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
+
Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing
by Cotlar, Ferguson, Sadosky (multi-parameter) of characterisation of
+
results, and talk about a few open problems.
spaces of bounded mean oscillation via L^p boundedness of commutators.
+
We present here an endpoint to this theory, bringing all such
+
characterisation results under one roof.
+
  
The tools used go deep into modern advances in dyadic harmonic
+
=== Oct 5: Eyal Subag (Penn State)===
analysis, while preserving the Ansatz from classical operator theory.
+
  
===November 1: Shaoming Guo (Indiana) ===
+
Symmetries of the hydrogen atom and algebraic families
Title: Parsell-Vinogradov systems in higher dimensions
+
  
Abstract:
+
The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry.  In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden,  give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system.  No prior knowledge on quantum mechanics or representation theory will be assumed.
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions.
+
Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hyper-surface will be discussed.
+
Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.
+
  
===November 17:Yevgeny Liokumovich (MIT)===
+
=== Oct 12: Andrei Caldararu (Madison)===
Title: Recent progress in Min-Max Theory
+
  
Abstract:
+
Mirror symmetry and derived categories
Almgren-Pitts Min-Max Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of long-standing open problems in Geometry, Geometric Analysis and 3-manifold Topology have been solved using this method. I will explain the main ideas and challenges in Min-Max Theory with an emphasis on its quantitative aspect: what quantitative information about the geometry and topology of minimal hypersurfaces can be extracted from the theory?
+
  
===November 21:Michael Kemeny (Stanford)===
+
Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.
Title: The equations defining curves and moduli spaces
+
  
Abstract:
+
In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).
A projective variety is a subset of projective space defined by polynomial equations. One of the oldest problems in algebraic geometry is to give a qualitative description of the equations defining a variety, together with
+
the relations amongst them. When the variety is an algebraic curve (or Riemann surface), several conjectures
+
made since the 80s give a fairly good picture of what we should expect. I will describe a new variational approach to these conjectures,
+
which reduces the problem to studying cycles on Hurwitz space or on the moduli space of curves.
+
  
 +
===  Oct 19:  Jeremy Teitelbaum (U Connecticut)===
 +
Lessons Learned and New Perspectives:
 +
From Dean and Provost to aspiring Data Scientist
  
===November 27:Tristan Collins (Harvard)===
+
After more than 10 years in administration, including 9 as Dean of
Title: The J-equation and stability
+
Arts and Sciences and 1 as interim Provost at UConn, I have returned
 +
to my faculty position.  I am spending a year as a visiting scientist
 +
at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington,
 +
Connecticut, trying to get a grip on some of the mathematical problems
 +
of interest to researchers in cancer genomics.  In this talk, I will offer some personal
 +
observations about being a mathematician and a high-level administrator, talk a bit about
 +
the research environment at an independent research institute like JAX-GM, outline
 +
a few problems that I've begun to learn about, and conclude with a
 +
discussion of how these experiences have shaped my view of graduate training in mathematics.
  
Abstract: Donaldson and Chen introduced the J-functional in '99, and explained its importance in the existence problem for constant scalar curvature metrics on compact Kahler manifolds. An important open problem is to find algebro-geometric conditions under which the J-functional has a critical point.  The critical points of the J-functional are described by a fully-nonlinear PDE called the J-equation.  I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the J-equation.
+
=== Oct 26: Douglas Ulmer (Arizona)===
  
===December 5: Ryan Hynd (U Penn)===
+
One of the central concerns of arithmetic geometry is the study of
Title: Adhesion dynamics and the sticky particle system.
+
solutions of systems of polynomial equations where the solutions are
 +
required to lie in a "small" field such as the rational numbers.  I
 +
will explain the landscape of expectations and conjectures in this
 +
area, focusing on curves and their Jacobians over global fields
 +
(number fields and function fields), and then survey the progress made
 +
over the last decade in the function field case.  The talk is intended
 +
to be accessible to a wide audience.
  
Abstract:  The sticky particle system expresses the conservation of mass and
+
== Past Colloquia ==
momentum for a collection of particles that only interact via perfectly inelastic collisions. 
+
The equations were first considered in astronomy in a model for the expansion of
+
matter without pressure. These equations also play a central role in the theory of optimal
+
transport.  Namely, the geodesics in an appropriately metrized space of probability
+
measures correspond to solutions of the sticky particle system.  We will survey what is
+
known about solutions and discuss connections with Hamilton-Jacobi equations.
+
  
===December 8: Nan Chen (Courant, NYU)===
+
[[Colloquia/Blank|Blank]]
Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems
+
  
Abstract:
+
[[Colloquia/Spring2018|Spring 2018]]
A conditional Gaussian framework for uncertainty quantification, data assimilation and prediction of nonlinear turbulent dynamical systems will be introduced in this talk. Despite the conditional Gaussianity, the dynamics remain highly nonlinear and are able to capture strongly non-Gaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the real-time data assimilation and prediction.
+
 
+
The talk will include three applications of such conditional Gaussian framework. In the first part, a physics-constrained nonlinear stochastic model is developed, and is applied to predicting the Madden-Julian oscillation indices with strongly non-Gaussian intermittent features. The second part regards the state estimation and data assimilation of multiscale and turbulent ocean flows using noisy Lagrangian tracers. Rigorous analysis shows that an exponential increase in the number of tracers is required for reducing the uncertainty by a fixed amount. This indicates a practical information barrier. In the last part of the talk, an efficient statistically accurate algorithm is developed that is able to solve a rich class of high dimensional Fokker-Planck equation with strong non-Gaussian features and beat the curse of dimensions.
+
 
+
===December 11: Connor Mooney (ETH Zurich)===
+
Title: Regularity vs. Singularity for Elliptic and Parabolic Systems
+
 
+
Abstract:
+
Hilbert's 19th problem asks if minimizers of &ldquo;natural&rdquo; variational integrals are smooth. For the past century, this problem inspired fundamental regularity results for elliptic and parabolic PDEs. It also led to the construction of several beautiful counterexamples to regularity. The dichotomy of regularity vs. singularity is related to that of single PDE (the scalar case) vs. system of PDEs (the vectorial case), and low dimension vs. high dimension. I will discuss some interesting recent counterexamples to regularity in low-dimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.
+
 
+
===December 15: Roy Lederman (Princeton)===
+
Title: Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy (cryo-EM)
+
 
+
Abstract:
+
Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
+
+
Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging.
+
+
While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryo-EM produces measurements of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.
+
+
I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. “hyper-molecules,” the mathematical formulation of truly continuously heterogeneous molecules, 2. computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.
+
 
+
===December 18: Jenny Wilson (Stanford)===
+
Title: Stability in the homology of configuration spaces
+
 
+
Abstract:
+
This talk will illustrate some patterns in the homology of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.
+
 
+
===December 19: Alex Wright (Stanford)===
+
Title: Dynamics, geometry, and the moduli space of Riemann surfaces
+
 
+
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.
+
 
+
== Spring 2018 ==
+
 
+
{| cellpadding="8"
+
!align="left" | date 
+
!align="left" | speaker
+
!align="left" | title
+
!align="left" | host(s)
+
|-
+
| March 16
+
|[https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)
+
|[[# TBA|  TBA  ]]
+
| WIMAW
+
|
+
|-
+
|April 4 (Wednesday)
+
| [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)
+
|[[# TBA|  TBA  ]]
+
| Craciun
+
|
+
|-
+
| April 6
+
| Reserved
+
|[[# TBA|  TBA  ]]
+
| Melanie
+
|
+
|-
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| April 13
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== Spring Abstracts ==
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=== <DATE>: <PERSON> (INSTITUTION) ===
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Title: <TITLE>
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Abstract: <ABSTRACT>
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== Past Colloquia ==
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[[Colloquia/Blank|Blank Colloquia]]
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[[Colloquia/Fall2017|Fall 2017]]
  
 
[[Colloquia/Spring2017|Spring 2017]]
 
[[Colloquia/Spring2017|Spring 2017]]

Latest revision as of 16:57, 17 October 2018

Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

The calendar for spring 2019 can be found here.

Fall 2018

date speaker title host(s)
Sep 12 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Harry Potter's Cloak via Transformation Optics Li
Sep 14 Room 911 Gunther Uhlmann (Univ. of Washington) Distinguished Lecture series Journey to the Center of the Earth Li
Sep 21 Room 911 Andrew Stuart (Caltech) LAA lecture The Legacy of Rudolph Kalman Jin
Sep 28 Gautam Iyer (CMU) Stirring and Mixing Thiffeault
Oct 5 Eyal Subag (Penn State) Symmetries of the hydrogen atom and algebraic families Gurevich
Oct 12 Andrei Caldararu (Madison) Mirror symmetry and derived categories ...
Oct 19 Jeremy Teitelbaum (U Connecticut) Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist Boston
Oct 26 Douglas Ulmer (Arizona) Rational numbers, rational functions, and rational points Yang
Nov 2 Reserved for job talk TBA hosting faculty
Nov 9 Reserved for job talk TBA hosting faculty
Nov 16 Reserved for job talk TBA hosting faculty
Nov 30 Reserved for job talk TBA hosting faculty
Dec 7 Reserved for job talk TBA hosting faculty

Abstracts

Sep 12: Gunther Uhlmann (Univ. of Washington)

Harry Potter's Cloak via Transformation Optics

Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "traansformation optics" in a non-technical fashion n the so-called that has received the most attention in the scientific literature.

Sep 14: Gunther Uhlmann (Univ. of Washington)

Journey to the Center of the Earth

We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others.

The problem can be recast as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary by measuring the distance function between boundary points? This is the boundary rigidity problem. We will also consider the problem of determining the metric from the scattering relation, the so-called lens rigidity problem. The linearization of these problems involve the integration of a tensor along geodesics, similar to the X-ray transform.

We will also describe some recent results, join with Plamen Stefanov and Andras Vasy, on the partial data case, where you are making measurements on a subset of the boundary. No previous knowledge of Riemannian geometry will be assumed.

Sep 21: Andrew Stuart (Caltech)

The Legacy of Rudolph Kalman

In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate, the importance of this work continues to grow too. The lecture will describe this paper, and developments that have stemmed from it, revolutionizing fields such space-craft control, weather prediction, oceanography and oil recovery, and with potential for use in new fields such as medical imaging and artificial intelligence. Some mathematical details will be also provided, but limited to simple concepts such as optimization, and iteration; the talk is designed to be broadly accessible to anyone with an interest in quantitative science.

Sep 28: Gautam Iyer (CMU)

Stirring and Mixing

Mixing is something one encounters often in everyday life (e.g. stirring cream into coffee). I will talk about two mathematical aspects of mixing that arise in the context of fluid dynamics:

1. How efficiently can stirring "mix"?

2. What is the interaction between diffusion and mixing.

Both these aspects are rich in open problems whose resolution involves tools from various different areas. I present a brief survey of existing results, and talk about a few open problems.

Oct 5: Eyal Subag (Penn State)

Symmetries of the hydrogen atom and algebraic families

The hydrogen atom system is one of the most thoroughly studied examples of a quantum mechanical system. It can be fully solved, and the main reason why is its (hidden) symmetry. In this talk I shall explain how the symmetries of the Schrödinger equation for the hydrogen atom, both visible and hidden, give rise to an example in the recently developed theory of algebraic families of Harish-Chandra modules. I will show how the algebraic structure of these symmetries completely determines the spectrum of the Schrödinger operator and sheds new light on the quantum nature of the system. No prior knowledge on quantum mechanics or representation theory will be assumed.

Oct 12: Andrei Caldararu (Madison)

Mirror symmetry and derived categories

Mirror symmetry is a remarkable phenomenon, first discovered in physics. It relates two seemingly disparate areas of mathematics, symplectic and algebraic geometry. Its initial formulation was rather narrow, as a technique for computing enumerative invariants (so-called Gromov-Witten invariants) of symplectic varieties by solving certain differential equations describing the variation of Hodge structure of “mirror" varieties. Over the past 25 years this narrow view has expanded considerably, largely due to insights of M. Kontsevich who introduced techniques from derived categories into the subject. Nowadays mirror symmetry encompasses wide areas of mathematics, touching on subjects like birational geometry, number theory, homological algebra, etc.

In my talk I shall survey some of the recent developments in mirror symmetry, and I will explain how my work fits in the general picture. In particular I will describe an example of derived equivalent but not birational Calabi-Yau three folds (joint work with Lev Borisov); and a recent computation of a categorical Gromov-Witten invariant of positive genus (work with my former student Junwu Tu).

Oct 19: Jeremy Teitelbaum (U Connecticut)

Lessons Learned and New Perspectives: From Dean and Provost to aspiring Data Scientist

After more than 10 years in administration, including 9 as Dean of Arts and Sciences and 1 as interim Provost at UConn, I have returned to my faculty position. I am spending a year as a visiting scientist at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington, Connecticut, trying to get a grip on some of the mathematical problems of interest to researchers in cancer genomics. In this talk, I will offer some personal observations about being a mathematician and a high-level administrator, talk a bit about the research environment at an independent research institute like JAX-GM, outline a few problems that I've begun to learn about, and conclude with a discussion of how these experiences have shaped my view of graduate training in mathematics.

Oct 26: Douglas Ulmer (Arizona)

One of the central concerns of arithmetic geometry is the study of solutions of systems of polynomial equations where the solutions are required to lie in a "small" field such as the rational numbers. I will explain the landscape of expectations and conjectures in this area, focusing on curves and their Jacobians over global fields (number fields and function fields), and then survey the progress made over the last decade in the function field case. The talk is intended to be accessible to a wide audience.

Past Colloquia

Blank

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012