Rainwater Seminar
The Rainwater Seminar covers a broad range of topics in Modern Analysis, including Real and Complex Analysis, Geometric Measure Theory, Ergodic Theory and Geometric Dynamics. This reflects the recent trends and emerging areas in Non-Smooth Analysis and Geometry, characterized by interdisciplinary connections. Some examples of these areas are Gromov's hyperbolic spaces, measure metric spaces, dynamics on translation surfaces, Schramm's Stochastic Loewner Evolution, the Zipper algorithm for conformal mappings, fractals arising in PDE's and in Dynamics, and PDEs on non-smooth domains.
The seminar meets on Tuesdays at 1:30 in PDL C-401, and may last up to two hours. In a two hour session the first 30 minutes will provide a general introduction accessible to first and second year graduate students. Then there will be a 15-20 minute coffee break (at which time it is perfectly permissible to leave), followed by an hour talk.
The seminar reflects the interests of Jayadev Athreya, Don Marshall, Steffen Rohde, Stefan Steinerberger, Tatiana Toro and Bobby Wilson, and is currently organized by Don Marshall, Steffen Rohde and Hadrian Quan. Please direct your questions to dmarshall@uw.edu, rohde@math.washington.edu, or hadrianq@uw.edu.
Graduate students can register for a credit.
Past Events
- Finding Patterns and Arithmetic Progressions in Fractal Sets (Krystal Taylor (OSU)) -
- Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces (David Aulicino (Brooklyn College)) -
- Divisibility of integer Laurent polynomials and dynamical systems (Doug Lind (UW Seattle)) -
- Minimization problems for the first Dirichlet Laplacian eigenvalue with volume constraint (Pedra Andrade (Instituto Superior Técnico)) -
- Venetian blinds, digital sundials, efficient coverings, and Kakeya sets (Alan Chang (Washington University St Louis)) -
- The Favard Length and Cyclotomic Structure of Rational Product Cantor Sets (Caleb Marshall (UBC)) -
- Global well-posedness, long-time behavior of solutions, and the stabilization phenomenon for some fluid equations (Weinan Wang (University of Oklahoma)) -
- Diophantine approximation, statistics on translation surfaces, and equivariant processes (Albert Artiles (UW Seattle)) -
- Billiards in Polyhedra (Jayadev Athreya (UW Seattle)) -
- Sobolev inequalities, metric measure spaces, and degenerate elliptic PDEs. (Lyudmila Korobenko (Reed College)) -
- Piecewise geodesic Jordan curves on the sphere (Janne Junnila, University of Helsinki) -
- Wave dynamics and semiclassical analysis: from graphs to manifolds (Akshat Kumar (Instituto de Telecomunicações, Lisboa)) -
- Curve tangencies and maximal functions (Joshua Zahl, University of British Columbia) -
- The infinite trivalent tree and the developed deltoid (Steffen Rohde, University of Washington) -
- Invasion: robustness and universality (Cole Graham (Brown University)) -
- Geometric Function theory, Quasiconvexity and lower Semicontinuity (Daniel Faraco, Universidad Autonoma Madrid) -
- Probabilistic global flows for supercritical PDEs (Mouhamadou Sy, Johns Hopkins University) -
- Zeros of Steklov eigenfunctions (Stefano Decio, University of Minnesota) -
- Low dimensional Cantor sets with absolutely continuous harmonic measure (Cole Jeznach, University of Minnesota) -
- Non-embeddability of Carnot Groups into L^1 (Lisa Naples, Macalester College) -
- Lipschitz decompositions of the complements of bilaterally flat sets (Jared Krandel, Stony Brook University) -
- The Schr\”odinger convergence problem and the Mass Transference Principle (Daniel Eceizabarrena, University of Massachusetts Amherst) -
- Energy Optimization for k-particle Interactions on the Sphere (Ryan Matzke, Vanderbilt University) -
- A monotonicity approach to Pogorelov's Hessian estimates for Monge-Ampere equation (Yu Yuan, UW) -
- Anisotropic Preiss density (Max Goering, Max Planck Institute) -
- Stability of elliptic Harnack inequality (Zhen-Qing Chen, UW) -
- Rectifiability of flat singularities for mod(p) area-minimizing hypersurfaces (Anna Skorobogatova, Princeton University) -
- Lower bounds for the directional discrepancy (Michelle Mastrianni, University of Minnesota) -
- The box-counting dimension in one-dimensional random geometry of multiplicative cascades (Sascha Troscheit, University of Oulu) -
- Exceptional sets of orthogonal projections: Classical results and current research (Ryan Bushling, University of Washington) -
- Inverse boundary value problems for quasilinear hyperbolic equations on Lorentzian manifolds (Yang Zhang, University of Washington) -
- Josh Southerland's thesis defense (Josh Southerland, University of Washington) -
- David Simmons's thesis defense (David Simmons, University of Washington) -
- The bigraded Rumin complex (Jeffrey Case) -
- Fractional Dirac operators and Geometric reconstruction (Hadrian Quan) -
- Boundary and Curvature on Graphs (Stefan Steinerberger, University of Washington) -
- Global well-posedness for the fractional NLS on the unit disk (Xueying Yu, University of Washington) -
- Dirac operators and topological insulators (Alexis Drouot, University of Washington) -
- Counting special Lagrangian classes and semistable Mukai vectors for K3 surfaces (Heather Lee) -
- Carleson measure estimates for bounded harmonic functions (John Garnett, UCLA) -
- Multidimensional Scaling on Metric Measure Spaces (Lara Kassab, Colorado State University) -
- Survey on the Falconer distance set problem (Hong Wang, Institute for Advanced Study) -
- Counting social interactions for discrete subsets of the plane (Samantha Fairchild, University of Washington) -
- A Harnack inequality for weak solutions of anisotropic PDEs (Max Goering, University of Washington) -
- Length Spectral Rigidity of Flat and Hyperbolic Metrics (Marissa Loving, Georgia Tech) -
- Interface pinning and anisotropies arising from periodic homogenization (William Feldman, University of Utah) -
- Geodesic Currents and the Marked Length Spectrum (Noelle Sawyer, Southwestern University) -
- Quantitative decompositions of Lipschitz mappings (Raanan Schul, Stony Brook University) -
- Boundary unique continuation of Dini domains (Zihui Zhao, University of Chicago) -
- Random Walks on the Sphere and Linear Systems of Equations (Stefan Steinerberger, University of Washington) -
- Topological characterisations of Loewner traces (Yizheng Yuan, Berlin) -
- On p-ellipticity and connections to solvability of elliptic complex valued PDEs (Martin Dindos, Edinburgh) -
- Thurston maps with four postcritical points (Annina Iseli, UCLA) -
- The Riemannian Quantitative Isoperimetric Inequality (Max Engelstein, UMN) -
- General Exam (David Simmons, UW) -
- Loewner energy, determinants of Laplacians, and Brownian loop measure (Yilin Wang, MIT) -
- Regularity Bootstrapping for fourth order nonlinear equations ( Arunima Bhattacharya) -
- Moving Averages and Coboundaries in Dynamical Systems (Joseph Rosenblatt, Univ. Illinois) -
- A quantification of the Besicovitch projection theorem and its generalizations (Blair Davey, CUNY) -
- Weak-* stability and potential Navier-Stokes singularities (Dallas Albritton) -
- L^2 bounds for a maximal directional Hilbert transform (Jongchon Kim, UBC) -
- Wasserstein Distance in Analysis, Number Theory and PDEs (Stefan Steinerberger, Yale) -
- Working Seminar (overview of recent work of Logunov-Malinnikova) (Bobby Wilson, UW) -
- Uniformization of random surface and Liouville quantum gravity (Xin Sun, Columbia University) -
- Working Seminar (overview of recent work of Logunov-Malinnikova) (Bobby Wilson, UW) -
- Nonconvexity and compact containment of mean value sets for second order uniformly elliptic operators in divergence form (Niles Armstrong, Kansas State University) -
- Counting Conjugacy Classes: Groups Rebelling Against Dynamics (Catherine Pfaff, Queen's University) -
- Ancient collapsed solutions of mean curvature flow (Theodora Bourni, University of Tennessee ) -
- Regularity of soap films near the boundary (Guy David, University of Paris XI) -
- Uniformizing surfaces via discrete harmonic maps (Ryokichi Tanaka, Tohoku University) -
- Enumerating square-tiled surfaces in genus two. (Sunrose Shrestha, Tufts University) -
- Counting square-tiled surfaces with prescribed real and imaginary foliations (Francisco Arana Herrera, Stanford) -
- On the size of the singular set in the Stefan problem (Xavier Ros-Oton, Universität Zürich) -
- An Introduction to the Little Lip Function (Bruce Hanson, St. Olaf) -
- Borel Subsystems and Ergodic Universality for Compact Zd-systems via Specification and Beyond (Tom Meyerovitch, Ben-Gurion University of the Negev) -
- Some recent results about geometric variational problems (Yannick Sire, Johns Hopkins) -
- Combinatorial Problems Related to Automorphism Groups of Compact Riemann Surfaces (Charles Camacho, Oregon State) -
- TBA (Martin Dindos, Edinburgh) -
- Minimal surfaces by way of complex analysis (Franc Forstneric, University of Ljubljana) -
- Multi-phase problems for harmonic measure, harmonic polynomials, and platonic solids. (Matthew Badger) -
- Combinatorial Gauss-Bonnet Theorem and its applications (Byung-Geun Oh (Hanyang University, Republic of Korea)) -
- Low Regularity Solutions for Gravity Water Waves (Albert Ai (UC Berkeley)) -
- On the dimension of Furstenberg measure for SL(2,R) random matrix products and the Diophantine condition in matrix groups. (Boris Solomyak (University of Bar-Ilan )) -
- Anisotropic counterpart of Allard’s rectifiability theorem and Plateau problem. (Antonio De Rosa, Courant Institute) -
- Soap films with gravity and almost-minimal surfaces (Salvatore Stuvard, UT Austin) -
- TBA (Bobby Wilson, UW) -
- Geometric realization of cyclically branched covers over spheres (Dami Lee, UW) -
- Regularity of Weak Solutions to Linear Parabolic Systems with Measurable Coefficients (Simon Bortz, UW) -
- Uniform level set estimates for the first Dirichlet eigenfunction (Thomas Beck, University of North Carolina) -
- Homomorphisms of pure mapping class groups to the integers (Priyam Patel, UCSD) -
- TBA (Priyam Patel, UCSD) -
- C^ {1, α} Reifenberg Theorems for Sets and Measures (Silvia Ghinassi, Stony Brook ) -
- Equidistribution of expanding translates of shrinking curves and Dirichlet's approximation theorem (Pengyu Yang , Ohio State University) -
- Traveling along Hölder curves (Matthew Badger, University of Connecticut) -
- Siegel-Veech transforms are in L^2 (Jayadev Athreya, University of Washington) -
- Elliptic measures and the geometry of the domains (Zihui Zhao, University of Washington) -
- Automatic convexity and Ornstein's L-one noninequalities (Bernd Kirchheim, Universität Leipzig) -
- Stochastic Homogenization for Reaction-Diffusion Equations (Jessica Lin, McGill University) -
- Boundary Regularity for the Free Boundary in the One-phase Problem (Hector Chang-Lara, Columbia University) -
- Harmonic measure on sets of co-dimension larger than 1 (Guy David, Université Paris-Sud ) -
- Heat flow on snowballs (Mathav Murugan, The University of British Columbia, Vancouver) -
- The Zimmer Program (Sebastian Hurtado Salazar, University of Chicago) -
- The nodal set of solutions to sublinear equations (Nicola Soave, Politecnico di Milano) -
- (Uniform) rectifiability and (integral) Menger curvature (Max Goering, University of Washington) -
- Minimal Surfaces Close to a Plane and Two-Valued Harmonic Functions (Spencer Becker-Kahn, University of Washington) -
- From Period Coordinates to Teichmueller Distance (Ian Frankel, University of Chicago) -
- The 1-dimensional extension property in complex analysis (Mark Lawrence, Nazarbayev University) -
- On minimizers and critical points for anisotropic isoperimetric problems (Robin Neumayer, Northwestern University) -
- Introductory talk: Introduction to Layer Potentials. Main talk: A Singular Integral Approach to Two-Phase Free Boundary Problems (Simon Bortz, University of Minnesota) -
- Uniqueness of mean curvature flow through (some) singularities (Or Hershkovits, Stanford) -
- Dynamics, geometry, and the moduli space of Riemann surfaces (Alex Wright, Stanford) -
- A free boundary problem on three-dimensional cones (Mark Allen, Brigham Young University) -
- Random trees via conformal welding (Peter Lin, UW) -
- Asymptotically optimal shapes: the drum with lowest n-th frequency, and the ellipse enclosing the most lattice points (Richard Laugesen, University of Illinois) -
- Absolute continuity of harmonic measure on rough domains (Murat Akman, University of Connecticut) -
- Rectifiability of harmonic measure (Sasha Volberg, Michigan State University) -
- On number of collisions of billiard balls (Chris Burdzy, UW) -
- Conformally Invariant Measures on Simple Loops (Stéphane Benoist, Massachusetts Institute of Technology) -
- NOT theory (not knot theory) (Chris Bishop, SUNY Stony Brook) -
- Conformal laminations and trees (Steffen Rohde, University of Washington) -
- Conformal Growth Rates and Spectral Geometry on Unimodular Random Graphs (James Lee, University of Washington) -
- Reversibility of the Loewner energy (Yilin Wang, ETH Zurich) -