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−  __NOTOC__
 
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 = 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'''. 
   
−  == Fall 2013 ==  +  The calendar for spring 2019 can be found [[Colloquia/Spring2019here]]. 
 +  
 +  ==Spring 2019== 
   
 { 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) 
     
−  Sept 6  +  Jan 25 
−  [http://people.math.gatech.edu/~mbaker/ Matt Baker] (Georgia Institute of Technology)  +   [http://www.users.miamioh.edu/randrib/ Beata Randrianantoanina] (Miami University Ohio) WIMAW 
−  RiemannRoch for Graphs and Applications  +  [[#Beata Randrianantoanina (Miami University Ohio)  Some nonlinear problems in the geometry of Banach spaces and their applications ]] 
−  Ellenberg  +   Tullia Dymarz 
 +   
     
−  Sept 13  +  Jan 30 '''Wednesday''' 
−  [http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)  +   [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) 
−  A hop, skip, and a jump through the degrees of relative provability  +  [[#Lillian Pierce (Duke University)  Short character sums ]] 
 +   Boston and Street 
     
     
−  Sept 20  +  Jan 31 '''Thursday''' 
−  [http://www.math.neu.edu/people/profile/valeriotoledanolaredo Valerio Toledano Laredo] (Northeastern)  +   [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M) 
−  Flat connections and quantum groups  +  [[#Dean Baskin (Texas A&M)  Radiation fields for wave equations ]] 
−  Gurevich  +   Street 
 +   
     
−  '''Wed, Sept 25, 2:30PM in B139'''  +  Feb 1 
−  [http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)  +   [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University) 
−  Taylor Series in Homotopy Theory  +  [[# TBA TBA ]] 
−  Meyer  +   Qin 
−  
 +   
−  '''Wed, Sept 25''' (LAA lecture)
 
−  [http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
 
−  CommunicationAvoiding Algorithms for Linear Algebra and Beyond  
−  Gurevich  
     
−  '''Thurs, Sept 26''' (LAA lecture, Joint with Applied Algebra Seminar)  +  Feb 5 '''Tuesday''' 
−  [http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
 +   [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University) 
−  Implementing CommunicationAvoiding Algorithms
 +  [[# TBA TBA ]] 
−  Gurevich
 +   Denisov 
−  
 
−  Sept 27 (LAA lecture)
 
−  [http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)
 
−  Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays
 
−  Gurevich
 
−  
 
−  Oct 4
 
−  [http://www.math.tamu.edu/~sottile/ Frank Sottile] (Texas A&M)  
−  Galois groups of Schubert problems
 
−  Caldararu
 
−  
 
−  Oct 11
 
−  [http://math.uchicago.edu/~wilkinso/ Amie Wilkinson] (Chicago)  
−  [[Colloquia#October 11: Amie Wilkinson (Chicago)  Robust mechanisms for chaos]]
 
−  WIMAW (Cladek)  
−  
 
−  '''Tues, Oct 15, 4PM''' (Distinguished Lecture)
 
−  [http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)
 
−  [[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT)  Integrable probability I]]
 
−  Valko
 
−  
 
−  '''Wed, Oct 16, 2:30PM''' (Distinguished Lecture)
 
−  [http://math.mit.edu/people/profile.php?pid=1222 Alexei Borodin] (MIT)
 
−  [[Colloquia#October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT)  Integrable probability II]]
 
−  Valko
 
−  
 
−  <strike>Oct 18</strike>
 
−  No colloquium due to the distinguished lecture
 
−  
 
     
     
−  Oct 25  +  Feb 8 
−  [http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)  +   [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern) 
−  [[Colloquia#October 25: Paul Garrett (Minnesota)  Boundaryvalue problems, generalized functions, and zeros of zeta functions]]  +  [[#Aaron Naber (Northwestern)  A structure theory for spaces with lower Ricci curvature bounds ]] 
−  Gurevich  +   Street 
−  
 
     
     
−  Nov 1  +  Feb 15 
−  [http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)  +   
−  On sets of large doubling, Lambda(4) sets, and errorcorrecting codes
 +  [[# TBA TBA ]] 
−  Stovall
 +   
−  
 
−  Nov 8
 
−  [http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)  
−  [[Colloquia#November 8: Tim Riley (Cornell)  Hydra groups]]
 
−  Dymarz  
−  
 
−  Nov 15 and later
 
−  Reserved
 
     
−  Street
 
−  
 
−  Nov 22
 
−  [http://www.math.uchicago.edu/~tj/ Tianling Jin] (University of Chicago)
 
−  Solutions of some MongeAmpere equations with degeneracy or singularities.
 
−  Bolotin
 
−  
 
−  '''Mon, Nov 25, 4PM'''
 
−  [https://web.math.princeton.edu/~linlin/ Lin Lin] (Lawrence Berkeley National Lab)
 
−  Fast algorithms for electronic structure analysis
 
−  Jin
 
     
−  '''Tue, Nov 26, 4PM, B139'''  +  Feb 22 
−  [http://www.math.cornell.edu/m/People/Faculty/conley Clinton Conley] (Cornell)  +   [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State) 
−  [[Colloquia#November 26 (Tuesday): Clinton Conley (Cornell)  Descriptive settheoretic graph theory]]
 +  [[# TBA TBA ]] 
−  Lempp
 +   Erman and Corey 
−  
 
−  '''Mon, Dec 2, 4PM'''
 
−  [http://www.math.northwestern.edu/~slm/ Simon Marshall] (Northwestern)
 
−  [[Colloquia#December 2 (Monday): Simon Marshall (Northwestern)  Semiclassical estimates for eigenfunctions on locally symmetric spaces]]  
−  Denissov
 
−  
 
−  '''Wed, Dec 4, 4PM'''
 
−  [http://math.berkeley.edu/~svs/ Steven Sam] (Berkeley)
 
−  Free Resolutions and Symmetry
 
−  Boston
 
−  
 
−  '''Fri, Dec 6'''
 
−  [http://math.mit.edu/~hand/ Paul Hand] (MIT)
 
−  [[Colloquia#December 6: Paul Hand (MIT)  Simplifications of the lifting approach for quadratic signal recovery problems]]
 
−  Thiffeault  
−  
 
−  '''Fri, Dec. 6 and Sat Dec. 7'''
 
     
−  [http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]
 
−  
 
−  
 
−  '''Mon, Dec. 9, 4pm, VV B239'''
 
−  [http://www.cims.nyu.edu/~jacob/ Jacob Bedrossian] (Courant Institute)
 
−  Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
 
−  Bolotin
 
−  
 
−  '''Wed, Dec 11, 4PM'''
 
−  [http://math.jhu.edu/~lwang/ Lu Wang] (Johns Hopkins)
 
−  Rigidity of Selfshrinkers of Mean Curvature Flow
 
−  Viaclovsky
 
−  
 
−  '''Fri, Dec. 13, 2:25pm, VV 901'''
 
−  [http://chanwookim.wordpress.com/ Chanwoo Kim] (Cambridge)
 
−  Regularity of the Boltzmann equation in convex domains
 
−  Bolotin
 
−  
 
−  '''Tues, Dec 17, 4PM'''
 
−  [http://www.statslab.cam.ac.uk/~ps422/ Perla Sousi] (Cambridge)
 
−  [[Colloquia#December 17: Perla Sousi (Cambridge)  The effect of drift on the volume of the Wiener sausage]]
 
−  Seppalainen
 
−  
 
−  '''Wed, Dec 18, 4PM'''
 
−  [http://users.math.yale.edu/~dc597/ Dustin Cartwright] (Yale)
 
−  [[Colloquia#December 18: Dustin Cartwright (Yale)  Tropical Complexes]]
 
−  Gurevich
 
−  }
 
− 
 
−  == Spring 2014 ==
 
− 
 
−  { cellpadding="8"
 
−  !align="left"  date
 
−  !align="left"  speaker
 
−  !align="left"  title
 
−  !align="left"  host(s)
 
−  
 
−  '''Mon, Jan 6, 4PM'''
 
−  [http://wwwbcf.usc.edu/~lauda/Aaron_Laudas_Page/Home.html Aaron Lauda] (USC)
 
−  [[Colloquia#January 6: Aaron Lauda (USC)  An introduction to diagrammatic categorification]]
 
−  Caldararu
 
     
−  '''Wed, Jan 8, 4PM'''  +  March 4 
−  [http://www2.math.umd.edu/~kmelnick/ Karin Melnick] (Maryland)  +   [http://wwwusers.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture 
−  [[Colloquia#January 8: Karin Melnick (Maryland)  Normal forms for local flows on parabolic geometries]]
 +  [[# TBA TBA ]] 
−  Kent
 +   Kim 
−  
 
−  Jan 10, 4PM
 
−  [http://users.math.yale.edu/~yd82/ Yen Do] (Yale)
 
−  Convergence of Fourier series and multilinear analysis
 
−  Denissov
 
−  
 
−  '''Mon, Jan 13, 4pm'''
 
−  [http://math.stanford.edu/~wangyi/ Yi Wang] (Stanford)
 
−  Isoperimetric Inequality and Qcurvature
 
−  Viaclovsky
 
−  
 
−  '''Wen, Jan 15, 4pm'''
 
−  [http://www.maths.ox.ac.uk/people/profiles/wei.xiang Wei Xiang] (University of Oxford)
 
−  [[Colloquia#January 15: Wei Xiang (University of Oxford) Conservation Laws and Shock Waves]]
 
−  Bolotin
 
−  
 
−  '''Fri, Jan 17, 2:25PM, VV901'''
 
−  [http://www.math.dartmouth.edu/~gillmana/ Adrianna Gillman] (Dartmouth)
 
−  Fast direct solvers for linear partial differential equations
 
−  Thiffeault
 
−  
 
−  '''Thu, Jan 23, 2:25, VV901'''
 
−  [http://www.stat.berkeley.edu/~mshkolni/ Mykhaylo Shkolnikov] (Berkeley)
 
−  [[Colloquia#Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley)  Intertwinings, wave equations and growth models]]  
−  Seppalainen  
−  
 
−  Jan 24
 
−  [http://www.yanivplan.com/ Yaniv Plan] (Michigan)
 
−  [http://www.math.wisc.edu/wiki/index.php/Applied/ACMS/absS14#Yaniv_Plan_.28Michigan.29 Lowdimensionality in mathematical signal processing]
 
−  Thiffeault
 
−  
 
−  Jan 31
 
−  [http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)
 
−  Underwater Networks: A Convergence of Communications, Control and Sensing
 
−  Gurevich
 
−  
 
−  Feb 7
 
−  David Treumann (Boston College)
 
−  Functoriality, Smith theory, and the Brauer homomorphism
 
−  Street
 
−  
 
−  Feb 14
 
−  [http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)
 
−  History of Mathematics Education as a Research Field and as Magistra Vitae
 
−  Kiselev
 
−  
 
−  Feb 21
 
−  [http://www.math.uci.edu/~szhitomi/ Svetlana Jitomirskaya] (UCIrvine)
 
−  Analytic quasiperiodic cocycles
 
−  Kiselev
 
−  
 
−  Feb 28
 
−  [http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)
 
     
−  Spagnolie
 
     
−  March 7  +  March 8 
−  [http://www.math.northwestern.edu/people/facultyProfiles/steve.zelditch.html Steve Zelditch] (Northwestern)  +   [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State) 
 +  [[# TBA TBA ]] 
 +   Erman 
     
−  Seeger
 
     
−  March 14  +  March 15 
−    +   Maksym Radziwill (Caltech) 
−    +  [[# TBA TBA ]] 
−  
 +   Marshall 
−  
 
−  <strike>March 21</strike>
 
−  '''Spring Break'''  
−  No Colloquium  
     
     
−  March 28  +  March 29 
−  [http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)  +   Jennifer Park (OSU) 
−  The Two Weight Inequality for the Hilbert Transform  +  [[# TBA TBA ]] 
−  Street  +   Marshall 
−    
−  April 4
 
−  [http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)
 
     
−  MariBeffa
 
     
−  April 11  +  April 5 
−  [http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)  +   JuLee Kim (MIT) 
 +  [[# TBA TBA ]] 
 +   Gurevich 
     
−  Gurevich
 
     
−  April 18 (Wasow Lecture)  +  April 12 
−  [http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)  +   Evitar Procaccia (TAMU) 
 +  [[# TBA TBA ]] 
 +   Gurevich 
     
−  Seeger
 
     
−  April 25  +  April 19 
−  [http://www.charlesdoran.net Charles Doran](University of Alberta)  +   [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University) 
 +  [[# TBA TBA ]] 
 +   JeanLuc 
     
−  Song
 
     
−  '''Monday, April 28''' (Distinguished Lecture)  +  April 26 
−  [http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)  +   [https://www.brown.edu/academics/appliedmathematics/faculty/kavitaramanan/home Kavita Ramanan] (Brown University) 
−  A mystery concerning algebraic plane curves
 +  [[# TBA TBA ]] 
−  Maxim
 +   WIMAW 
−  
 
−  '''Tuesday, April 29''' (Distinguished Lecture)
 
−  [http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
 
−  Matrix factorizations old and new
 
−  Maxim
 
−  
 
−  '''Wednesday, April 30''' (Distinguished Lecture)
 
−  [http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)  
−  Easy solution of polynomial equations over finite fields  
−  Maxim  
−  
 
−  May 2
 
−  [http://www.stat.uchicago.edu/~lekheng/ LekHeng Lim] (Chicago)
 
     
−  Boston
 
     
−  May 9  +  May 3 
−  [http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)  +   Tomasz Przebinda (Oklahoma) 
 +  [[# TBA TBA ]] 
 +   Gurevich 
     
−  WIMAW
 
 }   } 
   
 == Abstracts ==   == Abstracts == 
   
−  ===Sep 6: Matt Baker (GA Tech) ===  +  ===Beata Randrianantoanina (Miami University Ohio)=== 
−  ''RiemannRoch for Graphs and Applications''
 
   
−  We will begin by formulating the RiemannRoch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a RiemannRoch theorem for tropical curves, proved by GathmannKerber and MikhalkinZharkov, and a RiemannRoch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the BrillNoether theorem in algebraic geometry (work of by CoolsDraismaPayneRobeva), a "volumetheoretic proof" of Kirchhoff's MatrixTree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new ChabautyColeman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and ZureickBrown).
 +  Title: Some nonlinear problems in the geometry of Banach spaces and their applications. 
   
−  ===Sep 13: Uri Andrews (UWMadison) ===
 +  Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics. 
−  ''A hop, skip, and a jump through the degrees of relative provability''
 
   
−  The topic of this talk arises from two directions. On the one hand, Gödel's incompleteness theorem tell us that given any sufficiently strong, consistent, effectively axiomatizable theory T for firstorder arithmetic, there is a statement that is true but not provable in T. On the other hand, over the past seventy years, a number of researchers studying witnessing functions for various combinatorial statements have realized the importance of fastgrowing functions and the fact that their totality is often not provable over a given sufficiently strong, consistent, effectively axiomatizable theory T for firstorder arithmetic (e.g. the ParisHarrington and the KirbyParis theorems).
 +  ===Lillian Pierce (Duke University)=== 
   
−  I will talk about the structure induced by giving the order (for a fixed T) of relative provability for totality of algorithms. That is, for algorithms describing functions f and g, we say f ≤ g if T along with the totality of g suffices to prove the totality of f. It turns out that this structure is rich, and encodes many facets of the nature of provability over sufficiently strong, consistent, effectively axiomatizable theories for firstorder arithmetic. (Work joint with Mingzhong Cai, David Diamondstone, Steffen Lempp, and Joseph S. Miller.)
 +  Title: Short character sums 
   
−  ===Sep 20: Valerio Toledano Laredo (Northeastern)===
 +  Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a socalled character sum. For example, both understanding the Riemann zeta function or Dirichlet Lfunctions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations. 
−  ''Flat connections and quantum groups''
 
   
−  Quantum groups are natural deformations of the Lie algebra of
 +  ===Dean Baskin (Texas A&M)=== 
−  nxn matrices, and more generally of semisimple Lie algebras.
 
−  They first arose in the mid eighties in the study of solvable
 
−  models in statistical mechanics.
 
   
−  I will explain how these algebraic objects can serve as natural
 +  Title: Radiation fields for wave equations 
−  receptacles for the (transcendental) monodromy of flat connections
 
−  arising from representation theory.
 
   
−  These connections exist in rational, trigonometric and elliptic
 +  Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space. 
−  forms, and lead to quantum groups of increasing interest and
 
−  complexity.
 
   
−  ===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===  +  ===Aaron Naber (Northwestern)=== 
−  ''Taylor Series in Homotopy Theory''
 
   
−  I will discuss Goodwillie's calculus of functors on topological spaces. To mimic the setup in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation to a map between them, but a map allows us to construct the difference between two spaces, and two spaces are close if the difference between them is small. Spaces can be summed (in different ways) by taking twisted products of them. It is straightforward to construct the analogs of constant, linear, and higher degree homogenous functors, and they can be assembled into "polynomials" and "infinite sums". There are notions of differentiability and higher derivatives, of Taylor towers, and of analytic functions.
 +  Title: A structure theory for spaces with lower Ricci curvature bounds. 
   
−  What might look like a game of analogies is an extremely useful tool because when one looks at functors that map topological spaces not into the category of topological spaces, but into the category of spectra (the stabilized version of the category of spaces, which will be explained), many of them are, in fact, analytic, so they can be constructed from the homogenous functors of different degrees. And we can use appropriate analogs of calculus theorems to understand them better. I will conclude with some recent work of Randy McCarthy and myself, applying Goodwillie's calculus to algebraic Ktheory calculations.
 +  Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li. 
   
−  ===Sep 25: Jim Demmel (Berkeley) ===
 
−  ''Communication Avoiding Algorithms for Linear Algebra and Beyond''
 
   
−  Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct nbody simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices.
 +  == Past Colloquia == 
−   
−  ===Sep 26: Jim Demmel (Berkeley) ===  
−  ''Implementing Communication Avoiding Algorithms''
 
−   
−  Designing algorithms that avoiding communication, attaining
 
−  lower bounds if possible, is critical for algorithms to minimize runtime and
 
−  energy on current and future architectures. These new algorithms can have
 
−  new numerical stability properties, new ways to encode answers, and new data
 
−  structures, not just depend on loop transformations (we need those too!).
 
−  We will illustrate with a variety of examples including direct linear algebra
 
−  (eg new ways to perform pivoting, new deterministic and randomized
 
−  eigenvalue algorithms), iterative linear algebra (eg new ways to reorganize
 
−  Krylov subspace methods) and direct nbody algorithms, on architectures
 
−  ranging from multicore to distributed memory to heterogeneous.
 
−  The theory describing communication avoiding algorithms can give us a large
 
−  design space of possible implementations, so we use autotuning to find
 
−  the fastest one automatically. Finally, on parallel architectures one can
 
−  frequently not expect to get bitwise identical results from multiple runs,
 
−  because of dynamic scheduling and floating point nonassociativity;
 
−  this can be a problem for reasons from debugging to correctness.
 
−  We discuss some techniques to get reproducible results at modest cost.
 
−   
−  ===Sep 27: Jim Demmel (Berkeley) ===
 
−  ''Communication Lower Bounds and Optimal Algorithms for Programs that Reference Arrays''
 
−   
−  Our goal is to minimize communication, i.e. moving data, since it increasingly
 
−  dominates the cost of arithmetic in algorithms. Motivated by this, attainable
 
−  communication lower bounds have been established by many authors for a
 
−  variety of algorithms including matrix computations.
 
−   
−  The lower bound approach used initially by Irony, Tiskin and Toledo
 
−  for O(n^3) matrix multiplication, and later by Ballard et al
 
−  for many other linear algebra algorithms, depends on a geometric result by
 
−  Loomis and Whitney: this result bounds the volume of a 3D set
 
−  (representing multiplyadds done in the inner loop of the algorithm)
 
−  using the product of the areas of certain 2D projections of this set
 
−  (representing the matrix entries available locally, i.e., without communication).
 
−   
−  Using a recent generalization of Loomis' and Whitney's result, we generalize
 
−  this lower bound approach to a much larger class of algorithms,
 
−  that may have arbitrary numbers of loops and arrays with arbitrary dimensions,
 
−  as long as the index expressions are affine combinations of loop variables.
 
−  In other words, the algorithm can do arbitrary operations on any number of
 
−  variables like A(i1,i2,i22*i1,34*i3+7*i_4,…).
 
−  Moreover, the result applies to recursive programs, irregular iteration spaces,
 
−  sparse matrices, and other data structures as long as the computation can be
 
−  logically mapped to loops and indexed data structure accesses.
 
−   
−  We also discuss when optimal algorithms exist that attain the lower bounds;
 
−  this leads to new asymptotically faster algorithms for several problems.
 
−   
−  ===October 4: Frank Sottile (Texas A&M) ===
 
−  ''Galois groups of Schubert problems''
 
−   
−  Work of Jordan from 1870 showed how Galois theory
 
−  can be applied to enumerative geometry. Hermite earlier
 
−  showed the equivalence of Galois groups with geometric
 
−  monodromy groups, and in 1979 Harris used this to study
 
−  Galois groups of many enumerative problems. Vakil gave
 
−  a geometriccombinatorial criterion that implies a Galois
 
−  group contains the alternating group. With Brooks and
 
−  Martin del Campo, we used Vakil's criterion to show that
 
−  all Schubert problems involving lines have at least
 
−  alternating Galois group. White and I have given a new
 
−  proof of this based on 2transitivity.
 
−   
−  My talk will describe this background and sketch a
 
−  current project to systematically determine Galois groups
 
−  of all Schubert problems of moderate size on all small
 
−  classical flag manifolds, investigating at least several
 
−  million problems. This will use supercomputers employing
 
−  several overlapping methods, including combinatorial
 
−  criteria, symbolic computation, and numerical homotopy
 
−  continuation, and require the development of new
 
−  algorithms and software.
 
   
−  ===October 11: Amie Wilkinson (Chicago) ===
 +  [[Colloquia/BlankBlank]] 
   
−  ''Robust mechanisms for chaos''
 +  [[Colloquia/Fall2018Fall 2018]] 
   
−  What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?
 +  [[Colloquia/Spring2018Spring 2018]] 
   
−  In addressing this question, I'll focus on the study of diffeomorphisms of a compact manifold, where "chaotic" means "mixing" and and "robustly" means "stable under smooth perturbations." I'll describe recent advances in constructing and using tools called "blenders" to produce stably chaotic behavior with arbitrarily little effort.
 +  [[Colloquia/Fall2017Fall 2017]] 
   
−  ===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===
 +  [[Colloquia/Spring2017Spring 2017]] 
   
−  ''Integrable probability I and II''
 +  [[Archived Fall 2016 ColloquiaFall 2016]] 
   
−  The goal of the talks is to describe the emerging field of integrable
 +  [[Colloquia/Spring2016Spring 2016]] 
−  probability, whose goal is to identify and analyze exactly solvable
 
−  probabilistic models. The models and results are often easy to describe,
 
−  yet difficult to find, and they carry essential information about broad
 
−  universality classes of stochastic processes.
 
   
 +  [[Colloquia/Fall2015Fall 2015]] 
   
−  ===October 25: Paul Garrett (Minnesota)===
 +  [[Colloquia/Spring2014Spring 2015]] 
   
−  ''Boundaryvalue problems, generalized functions, and zeros of zeta functions''
 +  [[Colloquia/Fall2014Fall 2014]] 
   
−  Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years
 +  [[Colloquia/Spring2014Spring 2014]] 
−  ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)
 
−   
−  ===November 1: Allison Lewko (Columbia University) ===
 
−   
−  ''On sets of large doubling, Lambda(4) sets, and errorcorrecting codes''
 
−   
−  We investigate the structure of finite sets A of integers such that A+A is large, presenting a counterexample to natural conjectures in the pursuit of an "antiFreiman" theory in additive combinatorics. We will begin with a brief history of the problem and its connection to the study of Lambda(4) sets in harmonic analysis, and then we will discuss our counterexample and its construction from errorcorrecting codes. We will conclude by describing some related open problems.
 
−  This is joint work with Mark Lewko.
 
−   
−  ===November 8: Tim Riley (Cornell)===
 
−   
−  ''Hydra groups''
 
−   
−  A few years ago Will Dison and I constructed a family of
 
−  finitely generated groups whose workings include a stringrewriting
 
−  phenomenon of extraordinary duration which is reminiscent of Hercules'
 
−  battle with the hydra. I will describe this and the investigations it
 
−  spurred in hyperbolic geometry, combinatorial group theory, and a
 
−  problem of how to calculate efficiently with hugely compressed
 
−  representations of integers.
 
−   
−  ===November 22: Tianling Jin (University of Chicago)===
 
−   
−  ''Solutions of some MongeAmpere equations with degeneracy or singularities''
 
−   
−  We will first give a new proof of a celebrated theorem of
 
−  Jorgens which states that every classical convex solution of det(Hess
 
−  u)=1 in R^2 has to be a second order polynomial. Our arguments do not use
 
−  complex analysis, and will be applied to establish such Liouville type
 
−  theorems for solutions some degenerate MongeAmpere equations. We will
 
−  also discuss some results on existence, regularity, classification, and
 
−  asymptotic behavior of solutions of some MongeAmpere equations with
 
−  isolated and line singularities. This is joint work with J. Xiong.
 
−   
−  ===Monday, Nov 25: Lin Lin (Lawrence Berkeley National Lab)===
 
−   
−  ''Fast algorithms for electronic structure analysis''
 
−   
−  KohnSham density functional theory (KSDFT) is the most widely used
 
−  electronic structure theory for molecules and condensed matter systems. For
 
−  a system with N electrons, the standard method for solving KSDFT requires
 
−  solving N eigenvectors for an O(N) * O(N) KohnSham Hamiltonian matrix.
 
−  The computational cost for such procedure is expensive and scales as
 
−  O(N^3). We have developed pole expansion plus selected inversion (PEXSI)
 
−  method, in which KSDFT is solved by evaluating the selected elements of the
 
−  inverse of a series of sparse symmetric matrices, and the overall algorithm
 
−  scales at most O(N^2) for all materials including insulators,
 
−  semiconductors and metals. The PEXSI method can be used with orthogonal or
 
−  nonorthogonal basis set, and the physical quantities including electron
 
−  density, energy, atomic force, density of states, and local density of
 
−  states are calculated accurately without using the eigenvalues and
 
−  eigenvectors. The recently developed massively parallel PEXSI method has
 
−  been implemented in SIESTA, one of the most popular electronic structure
 
−  software using atomic orbital basis set. The resulting method can allow
 
−  accurate treatment of electronic structure in a unprecedented scale. We
 
−  demonstrate the application of the method for solving graphenelike
 
−  structures with more than 20,000 atoms, and the method can be efficiently
 
−  parallelized 10,000  100,000 processors on Department of Energy (DOE) high
 
−  performance machines.
 
−   
−  ===November 26 (Tuesday): Clinton Conley (Cornell)===
 
−   
−  ''Descriptive settheoretic graph theory''
 
−   
−  Familiar graphtheoretic problems (for example, vertex coloring) exhibit a
 
−  stark change of character when measurability constraints are placed on the
 
−  structures and functions involved. While discussing some ramifications in
 
−  descriptive set theory, we also pay special attention to interactions with
 
−  probability (concerning random colorings of Cayley graphs) and ergodic
 
−  theory (characterizing various dynamical properties of groups). The talk
 
−  will include joint work with Alexander Kechris, Andrew Marks, Benjamin
 
−  Miller, and Robin TuckerDrob.
 
−   
−   
−  ===December 2 (Monday): Simon Marshall (Northwestern)===
 
−   
−  ''Semiclassical estimates for eigenfunctions on locally symmetric spaces''
 
−   
−  Let M be a compact Riemannian manifold, and f an L^2normalised Laplace
 
−  eigenfunction on M. If p > 2, a theorem of Sogge tells us how large the L^p
 
−  norm of f can be in terms of its Laplace eigenvalue. For instance, when p
 
−  is infinity this is asking how large the peaks of f can be. I will present
 
−  an analogue of Sogge's theorem for eigenfunctions of the full ring of
 
−  invariant differential operators on a locally symmetric space, and discuss
 
−  some links between this result and number theory.
 
−   
−  ===December 4 (Wednesday): Steven Sam (Berkeley)===
 
−   
−  ''Free Resolutions and Symmetry''
 
−   
−  This talk is about the use of symmetry in the study of modules and free resolutions in commutative algebra and algebraic geometry, and specifically how it clarifies, organizes, and rigidifies calculations, and how it enables us to find finiteness in situations where it a priori does not seem to exist. I will begin the talk with an example coming from classical invariant theory and determinantal ideals using just some basic notions from linear algebra. Then I will explain some of my own work which builds on this setting in several directions. Finally, I'll discuss a recent program on twisted commutative algebras, developed jointly with Andrew Snowden, which formalizes the synthesis of representation theory and commutative algebra and leads to new finiteness results in seemingly infinite settings.
 
−   
−  ===December 6: Paul Hand (MIT)===
 
−   
−  ''Simplifications of the Lifting Approach for Quadratic Signal Recovery Problems''
 
−   
−  Many signal recovery problems are quadratic in nature, such as phase
 
−  retrieval and sparse principal component analysis. Such problems in
 
−  R^n can be convexified by introducing n^2 variables corresponding to
 
−  each quadratic combination of unknowns. This approach often gives
 
−  rise to an n x n matrix recovery problem that is convex and has
 
−  provable recovery guarantees. Because the dimensionality has been
 
−  squared, it is an important task to find simplifications that make
 
−  computation more tractable. We will discuss two examples where the
 
−  lifting approach can be simplified while retaining recovery
 
−  guarantees. These examples will be the phase retrieval problem and a
 
−  special case of sparse principal component analysis.
 
−   
−  ===December 9 (Monday): Jacob Bedrossian (Courant Institute)===
 
−   
−  ''Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations''
 
−   
−  We prove asymptotic stability of shear flows close to the
 
−  planar, periodic Couette flow in the 2D incompressible Euler equations.
 
−  That is, given an initial perturbation of the Couette flow small in a
 
−  suitable regularity class, specifically Gevrey space of class smaller than
 
−  2, the velocity converges strongly in L2 to a shear flow which is also
 
−  close to the Couette flow. The vorticity is asymptotically mixed to small
 
−  scales by an almost linear evolution and in general enstrophy is lost in
 
−  the weak limit. The strong convergence of the velocity field is sometimes
 
−  referred to as inviscid damping, due to the relationship with Landau
 
−  damping in the Vlasov equations. Joint work with Nader Masmoudi.
 
−   
−  ===Wednesday, Dec 11: Lu Wang (Johns Hopkins)===
 
−   
−  ''Rigidity of Selfshrinkers of Mean Curvature Flow''
 
−   
−  The study of mean curvature flow not only is fundamental in geometry, topology and analysis, but also has important applications in applied mathematics, for instance, image processing. One of the most important problems in mean curvature flow is to understand the possible singularities of the flow and selfshrinkers, i.e., selfshrinking solutions of the flow, provide the singularity models.
 
−   
−  In this talk, I will describe the rigidity of asymptotic structures of selfshrinkers. First, I show the uniqueness of properly embedded selfshrinkers asymptotic to any given regular cone. Next, I give a partial affirmative answer to a conjecture of Ilmanen under an infinite order asymptotic assumption, which asserts that the only twodimensional properly embedded selfshrinker asymptotic to a cylinder along some end is itself the cylinder. The feature of our results is that no completeness of selfshrinkers is required.
 
−   
−  The key ingredients in the proof are a novel reduction of unique continuation for elliptic operators to backwards uniqueness for parabolic operators and the Carleman type techniques. If time permits, I will discuss some applications of our approach to shrinking solitons of Ricci flow.
 
−   
−  ===Friday, Dec 13: Chanwoo Kim (Cambridge)===
 
−   
−  ''Regularity of the Boltzmann equation in convex domains''
 
−   
−  A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the nonlocal mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounceback and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical <math>C^{1}</math> solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct <math>W^{1,p}</math> solutions for 1< p<2 and weighted <math>W^{1,p}</math> solutions for <math>2\leq p\leq \infty</math> as well. On the other hand, we show second derivatives do not exist up to the boundary in general by constructing counterexamples for all boundary conditions. This is a joint work with Guo, Tonon, Trescases.
 
−   
−  ===December 17: Perla Sousi (Cambridge)===
 
−   
−  ''The effect of drift on the volume of the Wiener sausage''
 
−   
−  The Wiener sausage at time t is the algebraic sum of a Brownian path on [0,t] and a ball. Does the expected volume of the Wiener sausage increase when we add drift?
 
−  How do you compare the expected volume of the usual Wiener sausage to one defined as the algebraic sum of the Brownian path and a square (in 2D) or a cube (in higher dimensions)? We will answer these questions using their relation to the detection problem for Poisson Brownian motions, and rearrangement inequalities on the sphere (with Y. Peres). We will also discuss generalisations of this to Levy processes (with A. Drewitz and R. Sun) as well as an adversarial detection problem and its connections to Kakeya sets (with Babichenko, Peres, Peretz and Winkler).
 
−   
−   
−  ===December 18: Dustin Cartwright (Yale)===
 
−   
−  ''Tropical Complexes''
 
−   
−  Tropical geometry is a way of understanding algebraic varieties by the limiting behavior of their degenerations. Through tropicalization, algebraic operations are replaced with combinatorial constructions and piecewise linear functions. I will introduce tropical complexes, which a way of understanding the geometry of algebraic varieties through combinatorics. Tropical complexes are Deltacomplexes together with additional integral data, for which one has parallels and concrete comparisons with the behavior of algebraic varieties.
 
−   
−  ===January 6: Aaron Lauda (USC)===
 
−   
−  ''An introduction to diagrammatic categorification''
 
−   
−  Categorification seeks to reveal a hidden layer in mathematical
 
−  structures. Often the resulting structures can be combinatorially
 
−  complex objects making them difficult to study. One method of
 
−  overcoming this difficulty, that has proven very successful, is to
 
−  encode the categorification into a diagrammatic calculus that makes
 
−  computations simple and intuitive.
 
−   
−  In this talk I will review some of the original considerations that
 
−  led to the categorification philosophy. We will examine how the
 
−  diagrammatic perspective has helped to produce new categorifications
 
−  having profound applications to algebra, representation theory, and
 
−  lowdimensional topology.
 
−   
−  ===January 8: Karin Melnick (Maryland)===
 
−   
−  ''Normal forms for local flows on parabolic geometries''
 
−   
−  The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.
 
−   
−  ===January 10, 4PM: Yen Do (Yale)===
 
−   
−  ''Convergence of Fourier series and multilinear analysis''
 
−   
−  Almost everywhere convergence of the Fourier series of square
 
−  integrable functions was first proved by Lennart Carleson in 1966, and
 
−  the proof has lead to deep developments in various multilinear settings.
 
−  In this talk I would like to introduce a brief history of the subject
 
−  and sketch some recent developments, some of these involve my joint
 
−  works with collaborators.
 
−   
−  ===Mon, January 13: Yi Wang (Stanford)===
 
−   
−  ''Isoperimetric Inequality and Qcurvature''
 
−   
−  A wellknown question in differential geometry is to prove the
 
−  isoperimetric inequality under intrinsic curvature conditions. In
 
−  dimension 2, the isoperimetric inequality is controlled by the integral of
 
−  the positive part of the Gaussian curvature. In my recent work, I prove
 
−  that on simply connected conformally flat manifolds of higher dimensions,
 
−  the role of the Gaussian curvature can be replaced by the Branson's
 
−  Qcurvature. The isoperimetric inequality is valid if the integral of the
 
−  Qcurvature is below a sharp threshold. Moreover, the isoperimetric
 
−  constant depends only on the integrals of the Qcurvature. The proof
 
−  relies on the theory of $A_p$ weights in harmonic analysis.
 
−   
−  ===January 15: Wei Xiang (University of Oxford)===
 
−   
−  ''Conservation Laws and Shock Waves''
 
−   
−  The study of continuum physics gave birth to the theory of quasilinear
 
−  systems in divergence form, commonly called conservation laws. In this
 
−  talk, conservation laws, the Euler equations, and the definition of the
 
−  corresponding weak solutions will be introduced first. Then a short history
 
−  of the studying of conservation laws and shock waves will be given. Finally
 
−  I would like to present two of our current research projects. One is on the
 
−  mathematical analysis of shock diffraction by convex cornered wedges, and
 
−  the other one is on the validation of weakly nonlinear geometric optics for
 
−  entropy solutions of nonlinear hyperbolic systems of conservation laws.
 
−   
−  Fri, Jan 17, 2:25PM, VV901 Adrianna Gillman (Dartmouth) Fast direct solvers for linear partial differential equations
 
−   
−  ===Fri, Jan 17: Adrianna Gillman (Dartmouth) ===
 
−  ''Fast direct solvers for linear partial differential equations''
 
−   
−  The cost of solving a large linear system often determines what can and cannot be modeled computationally in many areas of science and engineering. Unlike Gaussian elimination which scales cubically with the respect to the number of unknowns, fast direct solvers construct an inverse of a linear in system with a cost that scales linearly or nearly linearly. The fast direct solvers presented in this talk are designed for the linear systems arising from the discretization of linear partial differential equations. These methods are more robust, versatile and stable than iterative schemes. Since an inverse is computed, additional righthand sides can be processed rapidly. The talk will give the audience a brief introduction to the core ideas, an overview of recent advancements, and it will conclude with a sampling of challenging application examples including the scattering of waves.
 
−   
−  ===Thur, Jan 23: Mykhaylo Shkolnikov (Berkeley) ===
 
−  ''Intertwinings, wave equations and growth models''
 
−   
−  We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to hyperbolic partial differential equations, symmetric polynomials and the corresponding random growth models. The talk will be devoted to these recent developments which also shed new light on some beautiful old examples of intertwinings. Based on joint works with Vadim Gorin and Soumik Pal.
 
−   
−   
−  ===Jan 24: Yaniv Plan (Michigan) ===
 
−  ''Lowdimensionality in mathematical signal processing''
 
−   
−  Natural images tend to be compressible, i.e., the amount of information needed to encode an image is small. This conciseness of information  in other words, low dimensionality of the signal  is found throughout a plethora of applications ranging from MRI to quantum state tomography. It is natural to ask: can the number of measurements needed to determine a signal be comparable with the information content? We explore this question under modern models of lowdimensionality and measurement acquisition.
 
−   
−  ===Thur, Jan 30: Urbashi Mitra (USC) ===
 
−  ''Underwater Networks: A Convergence of Communications, Control and Sensing''
 
−   
−  The oceans cover 71% of the earth’s surface and represent one of the least explored frontiers, yet the oceans are integral to climate regulation, nutrient production, oil retrieval and transportation. Future scientific and technological efforts to achieve better understanding of oceans and waterrelated applications will rely heavily on our ability to communicate reliably between instruments, vehicles (manned and unmanned), human operators, platforms and sensors of all types. Underwater acoustic communication techniques have not reached the same maturity as those for terrestrial radio communications and present some unique opportunities for new developments in information and communication theories. Key features of underwater acoustic communication channels are examined: slow speed of propagation, significant delay spreads, sparse multipath, timevariation and rangedependent available bandwidth. Another unique feature of underwater networks is that the cost of communication, sensing and control are often comparable resulting in new tradeoffs between these activities. We examine some new results (with implications wider than underwater systems) in channel identifiability, communicating over channels with state and cooperative game theory motivated by the underwater network application.
 
−   
−  ===Feb 7: David Treumann (Boston College) ===
 
−  ''Functoriality, Smith theory, and the Brauer homomorphism''
 
−   
−  Smith theory is a technique for relating the mod p homologies of X and of the fixed points of X by an automorphism of order p. I will discuss how, in the setting of locally symmetric spaces, it provides an easy method (no trace formula) for lifting mod p automorphic forms from G^{sigma} to G, where G is an arithmetic group and sigma is an automorphism of G of order p. This lift is compatible with Hecke actions via an analog of the Brauer homomorphism from modular representation theory, and is often compatible with a homomorphism of Lgroups on the Galois side. The talk is based on joint work with Akshay Venkatesh. I hope understanding the talk will require less number theory background than understanding the abstract.
 
−   
−  ===Feb 14: Alexander Karp (Columbia Teacher's College) ===
 
−  ''History of Mathematics Education as a Research Field and as Magistra Vitae''
 
−   
−  The presentation will be based on the experience of putting together and editing the Handbook
 
−  on the History of Mathematics Education, which will be published by Springer in the near future.
 
−  This volume, which was prepared by a large group of researchers from different countries,
 
−  contains the first systematic account of the history of the development of mathematics education
 
−  in the whole world (and not just in some particular country or region). The editing of such a
 
−  book gave rise to thoughts about the methodology of research in this field, and also about what
 
−  constitutes an object of such research. These are the thoughts that the presenter intends to share
 
−  with his audience. From them, it is natural to pass to an analysis of the current situation and how
 
−  it might develop.
 
−   
−  ===Feb 21: Svetlana Jitomirskaya (UCIrvine)===
 
−  ''Analytic quasiperiodic cocycles''
 
−   
−  Analytic quasiperiodic matrix cocycles is a simple dynamical
 
−  system, where analytic and dynamical properties are related in an
 
−  unexpected and remarkable way. We will focus on this relation, leading to
 
−  a new approach to the proof of joint continuity of Lyapunov exponents in
 
−  frequency and cocycle, at irrational frequency, first proved for SL(2,C)
 
−  cocycles in BourgainJitom., 2002. The approach is powerful enough to
 
−  handle singular and multidimensional cocycles, thus establishing the above
 
−  continuity in full generality. This has important consequences including
 
−  a dense open version of BochiViana theorem in this setting, with a
 
−  completely different underlying mechanism of the proof. A large part of
 
−  the talk is a report on a joint work with A. Avila and C. Sadel.
 
−   
−   
−  ===March 28: Michael Lacey (GA Tech) ===
 
−  ''The Two Weight Inequality for the Hilbert Transform''
 
−   
−  The individual two weight inequality for the Hilbert transform
 
−  asks for a real variable characterization of those pairs of weights
 
−  (u,v) for which the Hilbert transform H maps L^2(u) to L^2(v).
 
−  This question arises naturally in different settings, most famously
 
−  in work of Sarason. Answering in the positive a deep
 
−  conjecture of NazarovTreilVolberg, the mapping property
 
−  of the Hilbert transform is characterized by a triple of conditions,
 
−  the first being a twoweight Poisson A2 on the pair of weights,
 
−  with a pair of socalled testing inequalities, uniform over all
 
−  intervals. This is the first result of this type for a singular
 
−  integral operator. (Joint work with Sawyer, C.Y. Shen and UriateTuero)
 
−   
−  == Past Colloquia ==
 
   
 [[Colloquia/Fall2013Fall 2013]]   [[Colloquia/Fall2013Fall 2013]] 