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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.
Upcoming Events
March 26, 2024 - 1:30pm to 3:30pm
PDL C-401
Past Events
- Sobolev inequalities, metric measure spaces, and degenerate elliptic PDEs. (Lyudmila Korobenko (Reed College)) - November 28, 2023
- Piecewise geodesic Jordan curves on the sphere (Janne Junnila, University of Helsinki) - November 21, 2023
- Wave dynamics and semiclassical analysis: from graphs to manifolds (Akshat Kumar (Instituto de Telecomunicações, Lisboa)) - November 14, 2023
- Curve tangencies and maximal functions (Joshua Zahl, University of British Columbia) - November 7, 2023
- The infinite trivalent tree and the developed deltoid (Steffen Rohde, University of Washington) - October 31, 2023
- Invasion: robustness and universality (Cole Graham (Brown University)) - October 17, 2023
- Geometric Function theory, Quasiconvexity and lower Semicontinuity (Daniel Faraco, Universidad Autonoma Madrid) - October 10, 2023
- Probabilistic global flows for supercritical PDEs (Mouhamadou Sy, Johns Hopkins University) - May 30, 2023
- Zeros of Steklov eigenfunctions (Stefano Decio, University of Minnesota) - May 23, 2023
- Low dimensional Cantor sets with absolutely continuous harmonic measure (Cole Jeznach, University of Minnesota) - May 16, 2023
- Non-embeddability of Carnot Groups into L^1 (Lisa Naples, Macalester College) - May 9, 2023
- Lipschitz decompositions of the complements of bilaterally flat sets (Jared Krandel, Stony Brook University) - May 2, 2023
- The Schr\”odinger convergence problem and the Mass Transference Principle (Daniel Eceizabarrena, University of Massachusetts Amherst) - April 18, 2023
- Energy Optimization for k-particle Interactions on the Sphere (Ryan Matzke, Vanderbilt University) - April 11, 2023
- A monotonicity approach to Pogorelov's Hessian estimates for Monge-Ampere equation (Yu Yuan, UW) - March 28, 2023
- Anisotropic Preiss density (Max Goering, Max Planck Institute) - February 14, 2023
- Stability of elliptic Harnack inequality (Zhen-Qing Chen, UW) - February 7, 2023
- Rectifiability of flat singularities for mod(p) area-minimizing hypersurfaces (Anna Skorobogatova, Princeton University) - January 31, 2023
- Lower bounds for the directional discrepancy (Michelle Mastrianni, University of Minnesota) - November 15, 2022
- The box-counting dimension in one-dimensional random geometry of multiplicative cascades (Sascha Troscheit, University of Oulu) - November 8, 2022
- Exceptional sets of orthogonal projections: Classical results and current research (Ryan Bushling, University of Washington) - October 25, 2022
- Inverse boundary value problems for quasilinear hyperbolic equations on Lorentzian manifolds (Yang Zhang, University of Washington) - May 24, 2022
- Josh Southerland's thesis defense (Josh Southerland, University of Washington) - May 17, 2022
- David Simmons's thesis defense (David Simmons, University of Washington) - May 10, 2022
- The bigraded Rumin complex (Jeffrey Case) - April 19, 2022
- Fractional Dirac operators and Geometric reconstruction (Hadrian Quan) - March 29, 2022
- Boundary and Curvature on Graphs (Stefan Steinerberger, University of Washington) - March 8, 2022
- Global well-posedness for the fractional NLS on the unit disk (Xueying Yu, University of Washington) - February 22, 2022
- Dirac operators and topological insulators (Alexis Drouot, University of Washington) - February 8, 2022
- Counting special Lagrangian classes and semistable Mukai vectors for K3 surfaces (Heather Lee) - November 30, 2021
- Carleson measure estimates for bounded harmonic functions (John Garnett, UCLA) - October 26, 2021
- Multidimensional Scaling on Metric Measure Spaces (Lara Kassab, Colorado State University) - June 1, 2021
- Survey on the Falconer distance set problem (Hong Wang, Institute for Advanced Study) - May 25, 2021
- Counting social interactions for discrete subsets of the plane (Samantha Fairchild, University of Washington) - May 11, 2021
- A Harnack inequality for weak solutions of anisotropic PDEs (Max Goering, University of Washington) - May 4, 2021
- Length Spectral Rigidity of Flat and Hyperbolic Metrics (Marissa Loving, Georgia Tech) - April 13, 2021
- Interface pinning and anisotropies arising from periodic homogenization (William Feldman, University of Utah) - March 16, 2021
- Geodesic Currents and the Marked Length Spectrum (Noelle Sawyer, Southwestern University) - February 16, 2021
- Quantitative decompositions of Lipschitz mappings (Raanan Schul, Stony Brook University) - January 26, 2021
- Boundary unique continuation of Dini domains (Zihui Zhao, University of Chicago) - December 1, 2020
- Random Walks on the Sphere and Linear Systems of Equations (Stefan Steinerberger, University of Washington) - November 10, 2020
- Topological characterisations of Loewner traces (Yizheng Yuan, Berlin) - March 10, 2020
- On p-ellipticity and connections to solvability of elliptic complex valued PDEs (Martin Dindos, Edinburgh) - February 25, 2020
- Thurston maps with four postcritical points (Annina Iseli, UCLA) - February 4, 2020
- The Riemannian Quantitative Isoperimetric Inequality (Max Engelstein, UMN) - December 12, 2019
- General Exam (David Simmons, UW) - December 3, 2019
- Loewner energy, determinants of Laplacians, and Brownian loop measure (Yilin Wang, MIT) - November 27, 2019
- Regularity Bootstrapping for fourth order nonlinear equations ( Arunima Bhattacharya) - November 26, 2019
- Moving Averages and Coboundaries in Dynamical Systems (Joseph Rosenblatt, Univ. Illinois) - November 19, 2019
- A quantification of the Besicovitch projection theorem and its generalizations (Blair Davey, CUNY) - November 12, 2019
- Weak-* stability and potential Navier-Stokes singularities (Dallas Albritton) - November 5, 2019
- L^2 bounds for a maximal directional Hilbert transform (Jongchon Kim, UBC) - October 22, 2019
- Wasserstein Distance in Analysis, Number Theory and PDEs (Stefan Steinerberger, Yale) - October 15, 2019
- Working Seminar (overview of recent work of Logunov-Malinnikova) (Bobby Wilson, UW) - October 8, 2019
- Uniformization of random surface and Liouville quantum gravity (Xin Sun, Columbia University) - October 1, 2019
- Working Seminar (overview of recent work of Logunov-Malinnikova) (Bobby Wilson, UW) - September 24, 2019
- Nonconvexity and compact containment of mean value sets for second order uniformly elliptic operators in divergence form (Niles Armstrong, Kansas State University) - May 28, 2019
- Counting Conjugacy Classes: Groups Rebelling Against Dynamics (Catherine Pfaff, Queen's University) - May 21, 2019
- Ancient collapsed solutions of mean curvature flow (Theodora Bourni, University of Tennessee ) - May 14, 2019
- Regularity of soap films near the boundary (Guy David, University of Paris XI) - May 7, 2019
- Uniformizing surfaces via discrete harmonic maps (Ryokichi Tanaka, Tohoku University) - April 30, 2019
- Enumerating square-tiled surfaces in genus two. (Sunrose Shrestha, Tufts University) - April 23, 2019
- Counting square-tiled surfaces with prescribed real and imaginary foliations (Francisco Arana Herrera, Stanford) - April 16, 2019
- On the size of the singular set in the Stefan problem (Xavier Ros-Oton, Universität Zürich) - April 9, 2019
- An Introduction to the Little Lip Function (Bruce Hanson, St. Olaf) - March 26, 2019
- Borel Subsystems and Ergodic Universality for Compact Zd-systems via Specification and Beyond (Tom Meyerovitch, Ben-Gurion University of the Negev) - March 12, 2019
- Some recent results about geometric variational problems (Yannick Sire, Johns Hopkins) - March 5, 2019
- Combinatorial Problems Related to Automorphism Groups of Compact Riemann Surfaces (Charles Camacho, Oregon State) - February 26, 2019
- TBA (Martin Dindos, Edinburgh) - February 25, 2019
- Minimal surfaces by way of complex analysis (Franc Forstneric, University of Ljubljana) - February 19, 2019
- Multi-phase problems for harmonic measure, harmonic polynomials, and platonic solids. (Matthew Badger) - February 12, 2019
- Combinatorial Gauss-Bonnet Theorem and its applications (Byung-Geun Oh (Hanyang University, Republic of Korea)) - February 12, 2019
- Low Regularity Solutions for Gravity Water Waves (Albert Ai (UC Berkeley)) - February 5, 2019
- 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 )) - January 29, 2019
- Anisotropic counterpart of Allard’s rectifiability theorem and Plateau problem. (Antonio De Rosa, Courant Institute) - December 4, 2018
- Soap films with gravity and almost-minimal surfaces (Salvatore Stuvard, UT Austin) - November 27, 2018
- TBA (Bobby Wilson, UW) - November 20, 2018
- Geometric realization of cyclically branched covers over spheres (Dami Lee, UW) - November 13, 2018
- Regularity of Weak Solutions to Linear Parabolic Systems with Measurable Coefficients (Simon Bortz, UW) - November 6, 2018
- Uniform level set estimates for the first Dirichlet eigenfunction (Thomas Beck, University of North Carolina) - October 30, 2018
- TBA (Priyam Patel, UCSD) - October 16, 2018
- Homomorphisms of pure mapping class groups to the integers (Priyam Patel, UCSD) - October 16, 2018
- C^ {1, α} Reifenberg Theorems for Sets and Measures (Silvia Ghinassi, Stony Brook ) - October 9, 2018
- Equidistribution of expanding translates of shrinking curves and Dirichlet's approximation theorem (Pengyu Yang , Ohio State University) - May 22, 2018
- Traveling along Hölder curves (Matthew Badger, University of Connecticut) - May 15, 2018
- Siegel-Veech transforms are in L^2 (Jayadev Athreya, University of Washington) - May 8, 2018
- Elliptic measures and the geometry of the domains (Zihui Zhao, University of Washington) - May 1, 2018
- Automatic convexity and Ornstein's L-one noninequalities (Bernd Kirchheim, Universität Leipzig) - April 24, 2018
- Stochastic Homogenization for Reaction-Diffusion Equations (Jessica Lin, McGill University) - April 17, 2018
- Boundary Regularity for the Free Boundary in the One-phase Problem (Hector Chang-Lara, Columbia University) - April 10, 2018
- Harmonic measure on sets of co-dimension larger than 1 (Guy David, Université Paris-Sud ) - March 27, 2018
- Heat flow on snowballs (Mathav Murugan, The University of British Columbia, Vancouver) - March 6, 2018
- The Zimmer Program (Sebastian Hurtado Salazar, University of Chicago) - February 27, 2018
- The nodal set of solutions to sublinear equations (Nicola Soave, Politecnico di Milano) - February 20, 2018
- (Uniform) rectifiability and (integral) Menger curvature (Max Goering, University of Washington) - February 13, 2018
- Minimal Surfaces Close to a Plane and Two-Valued Harmonic Functions (Spencer Becker-Kahn, University of Washington) - February 6, 2018
- From Period Coordinates to Teichmueller Distance (Ian Frankel, University of Chicago) - December 5, 2017
- The 1-dimensional extension property in complex analysis (Mark Lawrence, Nazarbayev University) - November 28, 2017
- On minimizers and critical points for anisotropic isoperimetric problems (Robin Neumayer, Northwestern University) - November 14, 2017
- Introductory talk: Introduction to Layer Potentials. Main talk: A Singular Integral Approach to Two-Phase Free Boundary Problems (Simon Bortz, University of Minnesota) - October 31, 2017
- Uniqueness of mean curvature flow through (some) singularities (Or Hershkovits, Stanford) - October 24, 2017
- Dynamics, geometry, and the moduli space of Riemann surfaces (Alex Wright, Stanford) - October 17, 2017
- A free boundary problem on three-dimensional cones (Mark Allen, Brigham Young University) - October 10, 2017
- Random trees via conformal welding (Peter Lin, UW) - May 23, 2017
- Asymptotically optimal shapes: the drum with lowest n-th frequency, and the ellipse enclosing the most lattice points (Richard Laugesen, University of Illinois) - May 16, 2017
- Absolute continuity of harmonic measure on rough domains (Murat Akman, University of Connecticut) - May 9, 2017
- Rectifiability of harmonic measure (Sasha Volberg, Michigan State University) - May 2, 2017
- On number of collisions of billiard balls (Chris Burdzy, UW) - April 11, 2017
- Conformally Invariant Measures on Simple Loops (Stéphane Benoist, Massachusetts Institute of Technology) - March 28, 2017
- NOT theory (not knot theory) (Chris Bishop, SUNY Stony Brook) - February 23, 2017
- Conformal laminations and trees (Steffen Rohde, University of Washington) - February 14, 2017
- Conformal Growth Rates and Spectral Geometry on Unimodular Random Graphs (James Lee, University of Washington) - January 31, 2017
- Reversibility of the Loewner energy (Yilin Wang, ETH Zurich) - January 17, 2017