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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
 
−  [http://math.wisc.edu/~andrews/ Uri Andrews] (University of Wisconsin)
 
−  A hop, skip, and a jump through the degrees of relative provability  
     
     
−  Sept 20  +  Jan 30 '''Wednesday''' 
−  [http://www.math.neu.edu/people/profile/valeriotoledanolaredo Valerio Toledano Laredo] (Northeastern)
 +   [https://services.math.duke.edu/~pierce/ Lillian Pierce] (Duke University) 
−  Flat connections and quantum groups
 +  [[#Lillian Pierce (Duke University)  Short character sums ]] 
−  Gurevich
 +   Boston and Street 
−  
 
−  '''Wed, Sept 25, 2:30PM in B139'''
 
−  [http://mypage.iu.edu/~alindens/ Ayelet Lindenstrauss] (Indiana University)
 
−  Taylor Series in Homotopy Theory
 
−  Meyer
 
−  
 
−  '''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)
 
−  [http://www.cs.berkeley.edu/~demmel/ Jim Demmel] (Berkeley)  
−  Implementing CommunicationAvoiding Algorithms
 
−  Gurevich
 
−  
 
−  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  +  Jan 31 '''Thursday''' 
−  [http://www.math.umn.edu/~garrett/ Paul Garrett] (Minnesota)  +   [http://www.math.tamu.edu/~dbaskin/ Dean Baskin] (Texas A&M) 
−  Boundaryvalue problems, generalized functions, and zeros of zeta functions  +  [[#Dean Baskin (Texas A&M)  Radiation fields for wave equations ]] 
−  Gurevich  +   Street 
−    
     
     
−  Nov 1  +  Feb 1 
−  [http://www.cs.columbia.edu/~alewko/ Allison Lewko] (Columbia University)  +   [https://services.math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke University) 
−  On sets of large doubling, Lambda(4) sets, and errorcorrecting codes  +  [[# TBA TBA ]] 
−  Stovall  +   Qin 
−  
 
−  Nov 8  
−  [http://www.math.cornell.edu/~riley/ Tim Riley] (Cornell)
 
     
−  Dymarz
 
     
−  Nov 15 and later  +  Feb 5 '''Tuesday''' 
−  Reserved  +   [http://www.math.tamu.edu/~alexei.poltoratski/ Alexei Poltoratski] (Texas A&M University) 
 +  [[# TBA TBA ]] 
 +   Denisov 
     
−  Street
 
     
−  '''Fri, Dec. 6 and Sat Dec. 7'''  +  Feb 8 
−  No Seminar
 +   [https://sites.math.northwestern.edu/~anaber/ Aaron Naber] (Northwestern) 
−  [http://www.math.umn.edu/~stant001/askey80 Conference in honor of Dick Askey]  +  [[#Aaron Naber (Northwestern)  A structure theory for spaces with lower Ricci curvature bounds ]] 
 +   Street 
     
−  }
 
− 
 
−  == Spring 2014 ==
 
− 
 
−  { cellpadding="8"
 
−  !align="left"  date
 
−  !align="left"  speaker
 
−  !align="left"  title
 
−  !align="left"  host(s)
 
     
−  Jan 24  +  Feb 15 
−  [http://homepages.math.uic.edu/~mpopa/ Mihnea Popa] (UIC)  +   
 +  [[# TBA TBA ]] 
 +   
     
−  Arinkin
 
     
−  Jan 31  +  Feb 22 
−  [http://csi.usc.edu/~ubli/ubli.html Urbashi Mitra] (USC)  +   [https://people.math.osu.edu/cueto.5/ Angelica Cueto] (Ohio State) 
 +  [[# TBA TBA ]] 
 +   Erman and Corey 
     
−  Gurevich
 
     
−  Feb 7  +  March 4 
−  David Treumann (Boston College)  +   [http://wwwusers.math.umn.edu/~sverak/ Vladimir Sverak] (Minnesota) Wasow lecture 
 +  [[# TBA TBA ]] 
 +   Kim 
     
−  Street
 
     
−  Feb 14  +  March 8 
−  [http://www.tc.columbia.edu/academics/index.htm?facid=apk16 Alexander Karp] (Columbia Teacher's College)  +   [https://orion.math.iastate.edu/jmccullo/index.html Jason McCullough] (Iowa State) 
 +  [[# TBA TBA ]] 
 +   Erman 
     
−  Kiselev
 
     
−  Feb 21  +  March 15 
−  [http://math.nyu.edu/faculty/shelley/ Michael Shelley] (Courant)  +   Maksym Radziwill (Caltech) 
 +  [[# TBA TBA ]] 
 +   Marshall 
     
−  Spagnolie
 
     
−  Feb 28  +  March 29 
−    +   Jennifer Park (OSU) 
−    +  [[# TBA TBA ]] 
 +   Marshall 
     
     
−  March 7  +  April 5 
−    +   JuLee Kim (MIT) 
−    +  [[# TBA TBA ]] 
 +   Gurevich 
     
     
−  March 14  +  April 12 
−  Temporarily reserved  +   Evitar Procaccia (TAMU) 
−    +  [[# TBA TBA ]] 
−  Spagnolie
 +   Gurevich 
−  
 
−  <strike>March 21</strike>
 
−  '''Spring Break'''  
−  No Colloquium  
     
     
−  March 28
 +  April 19 
−  [http://people.math.gatech.edu/~lacey/ Michael Lacey] (GA Tech)
 +   [http://www.math.rice.edu/~jkn3/ Jo Nelson] (Rice University) 
−  The Two Weight Inequality for the Hilbert Transform
 +  [[# TBA TBA ]] 
−  Street
 +   JeanLuc 
−  
 
−  April 4  
−  [http://www.math.brown.edu/~res/ Richard Schwartz] (Brown)  
−    
−  MariBeffa  
−    
−  April 11
 
−  [http://www.cs.uchicago.edu/people/risi Risi Kondor] (Chicago)
 
     
−  Gurevich
 
     
−  April 18 (Wasow Lecture)  +  April 26 
−  [http://mathnt.mat.jhu.edu/sogge/ Christopher Sogge] (Johns Hopkins)  +   [https://www.brown.edu/academics/appliedmathematics/faculty/kavitaramanan/home Kavita Ramanan] (Brown University) 
 +  [[# TBA TBA ]] 
 +   WIMAW 
     
−  Seeger
 
     
−  April 25  +  May 3 
−  [http://www.charlesdoran.net Charles Doran](University of Alberta)  +   Tomasz Przebinda (Oklahoma) 
 +  [[# TBA TBA ]] 
 +   Gurevich 
     
−  Song
 
−  
 
−  '''Monday, April 28''' (Distinguished Lecture)
 
−  [http://www.msri.org/people/staff/de/ David Eisenbud](Berkeley)
 
−  A mystery concerning algebraic plane curves
 
−  Maxim
 
−  
 
−  '''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
 
−  [http://www.ma.utexas.edu/users/rward/ Rachel Ward] (UT Austin)
 
−  
 
−  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).
 
−   
−  ===Sep 13: Uri Andrews (UWMadison) ===
 
−  ''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).
 
−   
−  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.)
 
−   
−  ===Sep 20: Valerio Toledano Laredo (Northeastern)===
 
−  ''Flat connections and quantum groups''
 
−   
−  Quantum groups are natural deformations of the Lie algebra of
 
−  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
 
−  receptacles for the (transcendental) monodromy of flat connections
 
−  arising from representation theory.
 
−   
−  These connections exist in rational, trigonometric and elliptic
 
−  forms, and lead to quantum groups of increasing interest and
 
−  complexity.
 
−   
−  ===Wed, Sept 25, 2:30PM Ayelet Lindenstrauss (Indiana University)===
 
−  ''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.
 
−   
−  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.
 
−   
−  ===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.
 
−   
−  ===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
 +  Title: Some nonlinear problems in the geometry of Banach spaces and their applications. 
−  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
 +  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. 
−  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
 +  ===Lillian Pierce (Duke University)=== 
−  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;
 +  Title: Short character sums 
−  this leads to new asymptotically faster algorithms for several problems.
 
   
−  ===October 4: Frank Sottile (Texas A&M) ===
 +  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. 
−  ''Galois groups of Schubert problems''
 
   
−  Work of Jordan from 1870 showed how Galois theory
 +  ===Dean Baskin (Texas A&M)=== 
−  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
 +  Title: Radiation fields for wave equations 
−  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) ===
 +  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. 
   
−  ''Robust mechanisms for chaos''
 +  ===Aaron Naber (Northwestern)=== 
   
−  What are the underlying mechanisms for robustly chaotic behavior in smooth dynamics?
 +  Title: A structure theory for spaces with lower Ricci curvature bounds. 
   
−  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.  +  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. 
   
−  ===October 15 (Tue) and October 16 (Wed): Alexei Borodin (MIT) ===
 
   
−  ''Integrable probability I and II''
 +  == Past Colloquia == 
   
−  The goal of the talks is to describe the emerging field of integrable
 +  [[Colloquia/BlankBlank]] 
−  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/Fall2018Fall 2018]] 
   
−  ===October: Paul Garrett (Minnesota)===
 +  [[Colloquia/Spring2018Spring 2018]] 
   
−  ''Boundaryvalue problems, generalized functions, and zeros of zeta functions''
 +  [[Colloquia/Fall2017Fall 2017]] 
   
−  Modern analysis (Beppo Levi, Sobolev, Friedrichs, Schwartz) illuminates work of D. Hejhal and Y. Colin de Verdiere from 30 years
 +  [[Colloquia/Spring2017Spring 2017]] 
−  ago, clarifying, as in P. Cartier's letter to A. Weil, "how the Riemann Hypothesis was not proven". (Joint with E. Bombieri.)
 
   
 +  [[Archived Fall 2016 ColloquiaFall 2016]] 
   
 +  [[Colloquia/Spring2016Spring 2016]] 
   
−  ===November 1: Allison Lewko (Columbia University) ===
 +  [[Colloquia/Fall2015Fall 2015]] 
   
−  ''On sets of large doubling, Lambda(4) sets, and errorcorrecting codes''
 +  [[Colloquia/Spring2014Spring 2015]] 
   
−  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.
 +  [[Colloquia/Fall2014Fall 2014]] 
−  This is joint work with Mark Lewko.
 
   
−  ===March 28: Michael Lacey (GA Tech) ===
 +  [[Colloquia/Spring2014Spring 2014]] 
−  ''The Two Weight Inequality for the Hilbert Transform''
 
   
−  The individual two weight inequality for the Hilbert transform
 +  [[Colloquia/Fall2013Fall 2013]] 
−  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 talks ==
 +  [[Colloquia 20122013Spring 2013]] 
   
−  Last year's schedule: [[Colloquia 20122013]]
 +  [[Colloquia 20122013#Fall 2012Fall 2012]] 