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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 ColloquiaTentative schedule for next semester]] == >
 +  The calendar for spring 2019 can be found [[Colloquia/Spring2019here]]. 
−   +  
−  ==Fall 2017==
 +  
−   +  
−  { cellpadding="8"
 +  
−  !align="left"  Date
 +  
−  !align="left"  Speaker
 +  
−  !align="left"  Title
 +  
−  !align="left"  Host(s)
 +  
−  
 +  
−  September 8
 +  
−   [https://sites.google.com/a/wisc.edu/theresacanderson/home/ Tess Anderson] (Madison)
 +  
−  [[#September 8: Tess Anderson (Madison)  A Spherical Maximal Function along the Primes ]]
 +  
−   Tonghai Yang
 +  
−  
 +  
−  
 +  
−  September 15
 +  
−  
 +  
−  [[# ]]
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  September 22, '''9th floor'''
 +  
−   Jaeyoung Byeon (KAIST)
 +  
−  [[#September 22: Jaeyoung Byeon (KAIST)  Patterns formation for elliptic systems with large interaction forces ]]
 +  
−   Paul Rabinowitz & Chanwoo Kim
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  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'''
 +  
−   [http://www.tomokokitagawa.com/ Tomoko L. Kitagawa] (Berkeley)
 +  
−  [[#October 13: Tomoko Kitagawa (Berkeley)  A Global History of Mathematics from 1650 to 2017 ]]
 +  
−   Laurentiu Maxim
 +  
−  
 +  
−  
 +  
−  October 20
 +  
−   [http://cims.nyu.edu/~pgermain/ Pierre Germain] (Courant, NYU)
 +  
−  [[#October 13: Pierre Germain (Courant, NYU)  Stability of the Couette flow in the Euler and NavierStokes equations ]]
 +  
−   MinhBinh Tran
 +  
−  
 +  
−  
 +  
−  October 27
 +  
−  Stefanie Petermichl (Toulouse)
 +  
−  [[#October 27: Stefanie Petermichl (Toulouse)  Higher order Journé commutators ]]
 +  
−   Betsy Stovall, Andreas Seeger
 +  
−  
 +  
−  
 +  
−  November 1 (Wednesday)
 +  
−  [http://pages.iu.edu/~shaoguo/ Shaoming Guo] (Indiana)
 +  
−  [[#November 1: Shaoming Guo (Indiana) ParsellVinogradov systems in higher dimensions ]]
 +  
−  Andreas Seeger
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  
 +  
−  November 17
 +  
−   [http://math.mit.edu/~ylio/ Yevgeny Liokumovich] (MIT)
 +  
−  [[#November 17:Yevgeny Liokumovich (MIT) Recent progress in MinMax Theory ]]
 +  
−  Sean Paul
 +  
−  
 +  
−  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
 +  
−  '''Thanksgiving break'''
 +  
−  
 +  
−  
 +  
−  
 +  
−  November 27,
 +  
−   [http://www.math.harvard.edu/~tcollins/homepage.html Tristan Collins] (Harvard)
 +  
−  [[#November 27:Tristan Collins (Harvard) The Jequation and stability ]]
 +  
−  Sean Paul
 +  
−  
 +  
−  
 +  
−  
 +  
−  December 5 (Tuesday)
 +  
−   [http://web.sas.upenn.edu/rhynd/ Ryan Hynd] (U Penn)
 +  
−  [[#December 5: Ryan Hynd (U Penn) Adhesion dynamics and the sticky particle system]]
 +  
−  Sigurd Angenent
 +  
−  
 +  
−  
 +  
−  December 8 (Friday)
 +  
−   [https://cims.nyu.edu/~chennan/ Nan Chen] (Courant, NYU)
 +  
−  [[#December 8: Nan Chen (Courant, NYU) A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems ]]
 +  
−  Leslie Smith
 +  
−  
 +  
−  
 +  
−  
 +  
−  December 11 (Monday)
 +  
−   [https://people.math.ethz.ch/~mooneyc/ Connor Mooney] (ETH Zurich)
 +  
−  [[#December 11: Connor Mooney (ETH Zurich) Regularity vs. Singularity for Elliptic and Parabolic Systems]]
 +  
−  Sigurd Angenent
 +  
−  
 +  
−  
 +  
−  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 CryoElectron Microscopy (cryoEM) ]]
 +  
−  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 ==
 +  
−  === 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 GreenTao 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.
 +  
−   +  
−   +  
−  === September 22: Jaeyoung Byeon (KAIST) ===
 +  
−  Title: Patterns formation for elliptic systems with large interaction forces
 +  
−   +  
−  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, jth 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 2component systems, and then the much more complex case of 3component systems.
 +  
−   +  
−  ===October 6: Jonathan Hauenstein (Notre Dame) ===
 +  
−  Title: Real solutions of polynomial equations
 +  
−   +  
−  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 steadystate problems of hyperbolic conservation laws, solving semidefinite programs, and computing all steadystate solutions of the Kuramoto model.
 +  
−   +  
−  ===October 13: Tomoko Kitagawa (Berkeley) ===
 +  
−  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?
 +  
−   +  
−   +  
−   +  
−  ===October 20: Pierre Germain (Courant, NYU) ===
 +  
−  Title: Stability of the Couette flow in the Euler and NavierStokes equations
 +  
−   +  
−  Abstract: I will discuss the question of the (asymptotic) stability of the Couette flow in Euler and NavierStokes. 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 (BedrossianMasmoudi) and dimension 3 (BedrossianGermainMasmoudi).
 +  
−   +  
−  ===October 27: Stefanie Petermichl (Toulouse)===
 +  
−  Title: Higher order Journé commutators
 +  
−   +  
−  Abstract: We consider questions that stem from operator theory via Hankel and
 +  
−  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
 +  
−  nonnegative 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]=bHHb with the
 +  
−  Hilbert transform H=P_+  P_ . Whenever factorisation is absent, such
 +  
−  as in the real variable setting, in the multiparameter setting or
 +  
−  other, these classifications can be very difficult.
 +  
−   +  
−  Such lines were begun by Coifman, Rochberg, Weiss (real variables) and
 +  
−  by Cotlar, Ferguson, Sadosky (multiparameter) of characterisation of
 +  
−  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
 +  
−  analysis, while preserving the Ansatz from classical operator theory.
 +  
−   +  
−  ===November 1: Shaoming Guo (Indiana) ===
 +  
−  Title: ParsellVinogradov systems in higher dimensions
 +  
−   +  
−  Abstract:
 +  
−  I will present a few results on counting the numbers of integer solutions of ParsellVinogradov systems in higher dimensions.
 +  
−  Applications to Waring’s problem and to the problem of counting rational linear subspaces lying on certain hypersurface will be discussed.
 +  
−  Joint works with Jean Bourgain, Ciprian Demeter and Ruixiang Zhang.
 +  
−   +  
−  ===November 17:Yevgeny Liokumovich (MIT)===
 +  
−  Title: Recent progress in MinMax Theory
 +  
−   +  
−  Abstract:
 +  
−  AlmgrenPitts MinMax Theory is a method of constructing minimal hypersurfaces in Riemannian manifolds. In the last few years a number of longstanding open problems in Geometry, Geometric Analysis and 3manifold Topology have been solved using this method. I will explain the main ideas and challenges in MinMax 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)===
 +  
−  Title: The equations defining curves and moduli spaces
 +  
−   +  
−  Abstract:
 +  
−  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.
 +  
−   +  
−   +  
−  ===November 27:Tristan Collins (Harvard)===
 +  
−  Title: The Jequation and stability
 +  
−   +  
−  Abstract: Donaldson and Chen introduced the Jfunctional 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 algebrogeometric conditions under which the Jfunctional has a critical point. The critical points of the Jfunctional are described by a fullynonlinear PDE called the Jequation. I will discuss some recent progress on this problem, and indicate the role of algebraic geometry in proving estimates for the Jequation.
 +  
−   +  
−  ===December 5: Ryan Hynd (U Penn)===
 +  
−  Title: Adhesion dynamics and the sticky particle system.
 +  
−   +  
−  Abstract: The sticky particle system expresses the conservation of mass and
 +  
−  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 HamiltonJacobi equations.
 +  
−   +  
−  ===December 8: Nan Chen (Courant, NYU)===
 +  
−  Title: A Conditional Gaussian Framework for Uncertainty Quantification, Data Assimilation and Prediction of Complex Turbulent Dynamical Systems
 +  
−   +  
−  Abstract:
 +  
−  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 nonGaussian features such as intermittency and extreme events. The conditional Gaussian structure allows efficient and analytically solvable conditional statistics that facilitates the realtime data assimilation and prediction.
 +  
−   +  
−  The talk will include three applications of such conditional Gaussian framework. In the first part, a physicsconstrained nonlinear stochastic model is developed, and is applied to predicting the MaddenJulian oscillation indices with strongly nonGaussian 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 FokkerPlanck equation with strong nonGaussian 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 “natural” 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 lowdimensional vectorial cases, as well as outstanding open problems. Some of this is joint work with O. Savin.
 +  
−   +  
−  ===December 13: Bobby Wilson (MIT)===
 +  
−  Title: Projections in Banach Spaces and Harmonic Analysis
 +  
−   +  
−  Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections that follow from the classical BesicovitchFederer projection theorem. The BesicovitchFederer projection theorem offers a characterization of rectifiability of onedimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the BesicovitchFederer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinitedimensional and discuss related applications to questions in Harmonic Analysis. This is joint work with Marianna Csornyei and David Bate.
 +  
−   +  
−  ===December 15: Roy Lederman (Princeton)===
 +  
−  Title: Inverse Problems and Unsupervised Learning with applications to CryoElectron Microscopy (cryoEM)
 +  
−   +  
−  Abstract:
 +  
−  CryoEM 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 cryoelectron microscopy for the highresolution structure determination of biomolecules in solution".
 +  
− 
 +  
−  Cryoelectron microscopes produce a large number of very noisy twodimensional 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 xray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules together, cryoEM produces measurements of individual molecules. Therefore, cryoEM 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 cryoEM.
 +  
− 
 +  
−  I will discuss a onedimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryoEM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryoEM: 1. “hypermolecules,” 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 unsupervisedlearning component for recovering such hypermolecules in cryoEM.
 +  
−   +  
−  ===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 ktuples 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 representationtheoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higherorder stability phenomena  relationships between unstable homology classes in different degrees  established in recent work joint with Jeremy Miller. This project was inspired by workinprogress of GalatiusKupersRandalWilliams.
 +  
−   +  
−  ===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.
 +  == Fall 2018 == 
   
−  == Spring 2018 ==
 
   
 { cellpadding="8"   { cellpadding="8" 
Line 282: 
Line 14: 
 !align="left"  host(s)   !align="left"  host(s) 
     
−   March 16  +  Sep 12 '''Room 911''' 
−  [https://math.dartmouth.edu/~annegelb/ Anne Gelb] (Dartmouth)  +   [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series 
−  [[# TBA TBA ]]  +  [[#Sep 12: Gunther Uhlmann (Univ. of Washington) Harry Potter's Cloak via Transformation Optics ]] 
−   WIMAW  +   Li 
     
     
−  April 4 (Wednesday)  +  Sep 14 '''Room 911''' 
−   [http://math.ucr.edu/home/baez/ John Baez] (UC Riverside)  +   [https://sites.math.washington.edu/~gunther/ Gunther Uhlmann] (Univ. of Washington) Distinguished Lecture series 
−  [[# TBA TBA ]]  +  [[#Sep 14: Gunther Uhlmann (Univ. of Washington)  Journey to the Center of the Earth ]] 
−   Craciun  +   Li 
     
     
−   April 6  +  Sep 21 '''Room 911''' 
−   Reserved  +   [http://stuart.caltech.edu/ Andrew Stuart] (Caltech) LAA lecture 
−  [[# TBA TBA ]]  +  [[#Sep 21: Andrew Stuart (Caltech)  The Legacy of Rudolph Kalman ]] 
−   Melanie  +   Jin 
     
     
−   April 13  +  Sep 28 
−   [https://www.math.brown.edu/~jpipher/ Jill Pipher] (Brown)  +   [https://www.math.cmu.edu/~gautam/sj/index.html Gautam Iyer] (CMU) 
−  [[# TBA TBA ]]  +  [[#Sep 28: Gautam Iyer (CMU) Stirring and Mixing ]] 
−   WIMAW  +   Thiffeault 
     
     
−   April 25 (Wednesday)  +  Oct 5 
−   Hitoshi Ishii (Waseda University) Wasow lecture  +   [http://www.personal.psu.edu/eus25/ Eyal Subag] (Penn State) 
−  [[# TBA TBA ]]  +  [[#Oct 5: Eyal Subag (Penn State) Symmetries of the hydrogen atom and algebraic families ]] 
−   Tran  +   Gurevich 
     
     
−  date  +  Oct 12 
−   person (institution)  +   Arie Levit (Yale) 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
−   hosting faculty  +   Gurevich 
     
     
−  date  +  Oct 19 
−   person (institution)  +   Jeremy Teitelbaum (U Connecticut) 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
−   hosting faculty  +   Boston 
     
     
−  date  +  Oct 26 
−   person (institution)  +   Douglas Ulmer (Arizona) 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
−   hosting faculty  +   Yang 
     
     
−  date  +  Nov 2 
−   person (institution)  +   Reserved for job talk 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
  hosting faculty    hosting faculty 
     
     
−  date  +  Nov 9 
−   person (institution)  +   Reserved for job talk 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
  hosting faculty    hosting faculty 
     
     
−  date  +  Nov 16 
−   person (institution)  +   Reserved for job talk 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
  hosting faculty    hosting faculty 
     
     
−  date  +  Nov 30 
−   person (institution)  +   Reserved for job talk 
 [[# TBA TBA ]]   [[# TBA TBA ]] 
  hosting faculty    hosting faculty 
     
     
−  date  +  Dec 7 
−   person (institution)  +   Reserved for job talk 
−  [[# TBA TBA ]]
 +  
−   hosting faculty
 +  
−  
 +  
−  
 +  
−  date
 +  
−   person (institution)
 +  
 [[# TBA TBA ]]   [[# TBA TBA ]] 
  hosting faculty    hosting faculty 
Line 367: 
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 }   } 
   
−  == Spring Abstracts ==  +  == Abstracts == 
   
−  === <DATE>: <PERSON> (INSTITUTION) ===  +  === Sep 12: Gunther Uhlmann (Univ. of Washington) === 
−  Title: <TITLE>
 +  Harry Potter's Cloak via Transformation Optics 
   
−  Abstract: <ABSTRACT>
 +  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 nontechnical fashion 
 +  one of them, the socalled "traansformation optics" 
 +  in a nontechnical fashion n the socalled 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 socalled lens rigidity 
 +  problem. The linearization of these problems involve the integration 
 +  of a tensor along geodesics, similar to the Xray 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 spacecraft 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 HarishChandra 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. 
   
 == Past Colloquia ==   == Past Colloquia == 
   
−  [[Colloquia/BlankBlank Colloquia]]  +  [[Colloquia/BlankBlank]] 
 +  
 +  [[Colloquia/Spring2018Spring 2018]] 
 +  
 +  [[Colloquia/Fall2017Fall 2017]] 
   
 [[Colloquia/Spring2017Spring 2017]]   [[Colloquia/Spring2017Spring 2017]] 