The KCL analysis seminar is dedicated to all fields of mathematical analysis, from nonlinear PDEs to spectral theory, from probabilty theory to geometric analysis. It takes place on Thursdays at 11AM, KCL Strand Building, Room S5.20. If you want to be added to the mailing list contact one of the organisers: Jean Lagacé or Chia-Chun Lo (in either case, firstname.surname@kcl.ac.uk).
Title: Separating Recovering and Cancellative pairs and the Sandglass conjecture
Abstract. We address a basic extremal problem for pairs (A,B) of families of subsets of [n]. We say that a pair (A,B) is recovering, if for any two sets X, X' in A and any two sets Y, Y' in B, we have that X\Y = X'\Y' implies X=X' and Y\X=Y'\X' implies Y=Y'. We say that a pair (A,B) is cancellative if for any two sets X, X' in A and any two sets Y, Y' in B we have that X\Y = X'\Y implies X=X' and Y\X = Y'\X implies Y=Y'. It is easy to see that a cancellative pair is also recovering.
It was shown by Simonyi and by Nair and Yazdanpanah that 2^n ≤ |A||B| ≤ 2.266^n for any recovering pair (A,B). On the other hand, for cancellative pairs we have 2.25^n ≤ |A||B| ≤ 2.268^n, due to Tolhuizen and B. Janzer. However, it was unclear whether the quantity |A||B| for a recovering pair is smaller than the one for a cancellative pair. We show an exponential separation between the bounds for recovering and cancellative pairs. As a result, we improve the best known bound for recovering pairs.
(Joint work with Victor Souza and Leo Versteegen.)
May 1st
Speaker: Iveta Semoradova (Cardiff)
Title: Diverging eigenvalues in domain truncations of Schrödinger operators with complex potentials
May 8th
Speaker: Sam Farrington (Durham)
Title: Shape optimisation for Neumann eigenvalues
May 15th
Speaker: Adva Mond (KCL)
Title: Separating Recovering and Cancellative pairs and the Sandglass conjecture
January 16th:
Speaker: Alexander Pushnitski (King's College London)
Title: An inverse spectral problem for positive Hankel operators
January 23rd:
Speaker: Natalya Vaysfeld (King's College London)
Title: The Boundary Value Problem Approach to the Simulation of Porous Materials’ Stress State
January 30th:
Speaker: Arjun Sobnack (Warwick)
Title: Delayed parabolic regularity for the Curve Shortening Flow
February 6th: Break
February 13th:
Speaker: Anna Kononova (Tel Aviv)
Title: Zero and uniqueness sets for classes of entire functions
February 20th: Break
February 27th:
Speaker: Leonid Parnovski (UCL)
Title: Classical spectral asymptotics with a modern twist
March 6th:
Speaker: Alix Deleporte (Université Paris-Saclay)
Title: Spectral and heat observability on hyperbolic surfaces
March 13th:
Speaker: Sebastian Velazquez (KCL)
Title: Phase retrieval from short-time Fourier transform in locally compact abelian groups
March 20th:
Speaker: Nazar Miheisi (KCL)
Title: Averages with the divisor function
September 26th:
Speaker: Dmytro Karvatskyi (Institute of Mathematics of NAS of Ukraine & University of St. Andrews)
Title: Topological, metric, and fractal properties of the sets of subsums of convergent positive series
October 3rd:
Speaker: Cillian Doherty (Cambridge)
Title: On the Sobolev removability of the graph of one-dimensional Brownian motion
October 10th:
Speaker: Marius Tiba (King's)
Title: Stability of the Brunn-Minkowski inequality
October 17th:
Speaker: Chia-Chun Lo (King's)
Title: Homogenisation for the Robin problem on manifolds and flexibility of optimal Schrödinger potentials
October 24th: No talk
October 31st:
Speaker: Artemis Vogiatzi (Queen Mary)
Title: Quartically pinched submanifolds for the mean curvature flow in the sphere.
November 7th:
Speaker: Omar El-Fallah (Mohammed V University, Rabat)
Title: Dirichlet spaces and related problems
November 14th:
Speaker: Eliana Fausti (Imperial)
Title: The Hilbert projective metric and filtering stability
November 21th:
Speaker: Spencer Bullent (UCL)
Title: Weyl Law of the Steklov Problem on Piecewise Smooth Domains
November 28th:
Speaker: Daniel Seco (Univ. de La Laguna)
Title: A counterexample to the Weak Shanks Conjecture
December 5th:
Speaker: Boris Khoruzhenko (Queen Mary)
Title: Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series
April 25th:
Speaker: Purba Das (KCL)
Title: Invariance of Stochastic Integral
May 2nd:
Speaker: Víctor Navarro-Fernández (Imperial)
Title: Mixing and fast dynamo with random ABC flows
May 9th:
Speaker: Rocío Nores (University of Buenos Aires)
Title: The density of Gabor systems in expansible locally compact abelian groups
May 16th:
Speaker: Alex Bergman (Lund University)
Title: Invariant subspaces of generalized differentiation and Volterra operators
May 23rd:
Speaker: Jean Lagacé (KCL)
Title: Spectral decomposition on the space of flat surfaces: Laplacians and Siegel—Veech Transforms
May 30th:
Speaker: Dmitri Panov (KCL)
Title: Spherical surfaces
June 6th:
Speaker: Ghazaleh Asghari Khonakdari (Reading)
Title: Schatten class Hankel operators on doubling Fock spaces and the Berger-Coburn phenomenon
June 13th:
Speaker: Donnell Obovu (UCL)
Title: Resolvent bounds for Lipschitz potentials in dimensions two and higher with singularities at the origin
June 20th: Postponed to Autumn
Speaker: Natalya Vaysfeld (KCL)
Title: TBA
January 18th:
Speaker: Jared White (KCL)
Title: Weak*-closed ideals of dual Banach algebras on groups
January 25th:
Speaker: Zsuzsanna Baran (Cambridge)
Title: Phase transition for random walks on graphs with added weighted random matching
February 1st:
Speaker: Yury Dyukarev (KCL)
Title: The Nevanlinna Formula for the Pick Interpolation Problem
February 8th:
Speaker: Kobe Marshall-Stevens (UCL)
Title: On isolated singularities and generic regularity of min-max CMC hypersurfaces
February 15th:
Speaker: Joaquín Singer (University of Buenos Aires)
Title: Hadwiger's problem for convex bodies with enough sub-gaussian marginals
February 22nd:
Speaker: Abhay Jindal (IISc, Bangalore)
Title: Invariants associated with complete Nevanlinna-Pick spaces
February 29th:
Speaker: Elena Boguslavskaya (Brunel University London)
Title: Fractional order stochastic integral - is it possible?
March 7th:
Speaker: Megan Griffin-Pickering (UCL)
Title: The Vlasov-Poisson system for ions: stability and the quasineutral limit
March 14th:
Speaker: Robert Simon (LSE)
Title: Paradoxical Decompositions and Colouring Rules
March 21st:
Speaker: Alix Deleporte (Université Paris-Saclay, Orsay)
Title: Perspectives on the Widom conjecture
October 12th:
Speaker: Shubham Gupta (Imperial)
Title: Symmetrization inequalities on graphs
October 19th:
Speaker: Stephen Lynch (Imperial)
Title: Plateau's problem via the theory of phase transitions
October 26th:
Speaker: Eugene Shargorodsky (King's)
Title: Sharp estimates for conditionally centred moments and for compact operators on Lp spaces
November 2nd:
No talk. See OPSFOTA meeting.
November 9th:
Speaker: Amélie Loher (Cambridge)
Title: Existence results for the Landau equation
November 16th:
Speaker: Svetlana Malysheva (Queen Mary)
Title: Spectral properties of random matrices with heavy-tailed entries
November 23rd:
Speaker: Michael Levitin (Reading)
Title: New methods and results in two old problems
November 30th:
Speaker: Dave Smith (Yale-NUS College)
Title: Fokas Diagonalization
December 7th:
Speaker: Esther Bou Dagher (Imperial)
Title: Exponential inequalities in probability spaces revisited
January 19th:
Speaker: Naz Miheisi (KCL)
Title:
January 26th:
Speaker: Matthew Jenssen (KCL)
Title:
February 2nd:
Speaker: Hamed Mousavi (KCL)
Title:
February 9th:
Speaker: Cancelled
Title:
February 16th:
Speaker: Cancelled
Title:
February 23rd:
Speaker: Cancelled
Title:
March 2nd:
Speaker: Natalie Evans
Title: Correlations of almost primes
March 9th:
Speaker: Lashi Bandara
Title:
March 16th: --- No talk today
Speaker:
Title:
March 23rd:
Speaker: Felipe Marceca
Title: Perfect freezing and discrepancy estimates for Gaussian beta ensembles at the microscopic scale.
October 6th:
Speaker: Igor Wigman (KCL)
Title: The Robin problem on rectangles
October 13th:
Speaker: Sasha Pushnitski (KCL)
Title: Unbounded Hankel Operators
October 20th:
Speaker: Aled Walker (KCL)
Title: Higher order Fourier analysis, and linear inequalities
October 27th:
Speaker: Jean Lagacé (KCL)
Title: Statistics of cut-and-project sets via lattice point counting
November 3rd:
Speaker: Benjamin Doyon (KCL)
Title: Rigorous results in quantum statistical mechanics and hydrodynamics using operator algebras and Hilbert spaces
November 10th:
Speaker: Zoe Wyatt (KCL)
Title: The initial value problem in general relativity
November 17th:
Speaker: Ben Krause (KCL)
Title: Pointwise ergodic theory: examples and entropy
November 24th:
Speaker: Steve Lester (KCL)
Title: Spacing statistics for lattice points on circles
December 1st:
Speaker: Karl-Mikael Perfekt (NTNU, Norway)
Title: Hankel operators on Paley -- Wiener spaces in two dimensions
December 8th:
Speaker: Giuseppe Tinaglia (KCL)
Title: TBC