All talks are 15 minutes. Breaks are 5 or 10 minutes. Participation in this miniconference is by invitation only. Please see the Technical details page for essential pre-meeting steps. Remember to send your summary of key notation (up to 1 page) to Laugesen@illinois.edu, by Wednesday April 1, so that it can be distributed to all participants.
Preprint links are provided where possible. For a reprint of the journal version, please check your library or contact the author.
Thursday April 2
8:00-10:00pm EDT Optional technical pre-meeting (drop-in help session, join whenever you can)
Friday April 3 (All times in EDT Eastern Daylight Time, USA)
3:00 Welcome
3:05 Evans M. Harrell (Georgia Institute of Technology) – Complementary estimates for eigenvalue means – preprint – Harrell slides
3:20 question break
3:25 Jeffrey Langford (Bucknell University) – Exit time moments and eigenvalue estimates – preprint 2016 and preprint 2017 – Langford slides
3:40 question break
3:50 Richard S. Laugesen (University of Illinois at Urbana-Champaign) – Well-posedness of Weinberger’s center of mass by energy minimization – preprint – Laugesen slides
4:05 question break
4:10 Lotfi Hermi (Florida International University) – Isoperimetric inequalities for wedge-like membranes and convex cones –
4:25 question break
4:35 Derek Kielty (University of Illinois at Urbana-Champaign) – Spectral gaps of 1-dim Robin Schrödinger operators – paper expected on ArXiv by end of April
4:50 question break
4:55 Thomas Beck (University of North Carolina at Chapel Hill) – Eigenvalue estimates and localization of the first Dirichlet eigenfunction – preprint – Beck slides
5:10 question break
5:15 End of the session
Saturday April 4 (All times in EDT Eastern Daylight Time, USA)
10:00 Alexandre Girouard (Université Laval) – From Steklov to Neumann eigenvalues via homogenization – preprint – Girouard slides
10:15 question break
10:20 David Sher (DePaul University) – Steklov eigenvalue asymptotics for curvilinear polygons – preprint – Sher slides
10:35 question break
10:45 Javier Almonacid (Simon Fraser University) – Attractors and the spectrum of a zeroth-order pseudo-differential operator – Almonacid slides
11:00 question break
11:05 Michael Loss (Georgia Institute of Technology) – On the convolution inequality f ≥ f
* f
11:20 question break
11:30 Mark Ashbaugh (University of Missouri at Columbia) – Open Problems Session – Open problems
12:15 End of the session
2:00 Mikhail Karpukhin (University of California, Irvine) – Isoperimetric inequalities for Laplacian eigenvalues on surfaces – preprint 2017 and preprint 2019 – Karpukhin slides
2:15 question break
2:20 Xiaolong (Hans) Han (University of Illinois at Urbana-Champaign) – Eigenvalue estimate on geometrically finite hyperbolic manifolds with infinite volume – preprint – Han slides
2:35 question break
2:45 Selma Yildirim (University of Chicago) – Extensions of some results about the eigenvalues for the Laplacian – Yildirim slides
3:00 question break
3:05 Carlo Morpurgo (University of Missouri at Columbia) – Moser-Trudinger inequalities on Riesz subcritical domains and on Agmon-Souplet domains – preprint – Morpurgo slides
3:20 question break
3:30 Rafael Benguria (P. Universidad Católica de Chile) – Existence and non-existence of minimizers for Poincaré-Sobolev inequalities
3:45 question break
3:50 End of the session – conference photo (most people)
Other invited participants
Rodrigo Banuelos (Purdue University)
L. Mercredi Chasman (University of Minnesota at Morris)
Sebastian Dominguez (Simon Fraser University)
Michael Dotzel (Massachusetts Institute of Technology)
Ailana Fraser (University of British Columbia)
Hanna Kim (University of Illinois at Urbana-Champaign)
Jean Lagacé (University College, London)
Pat McDonald (New College, Florida)
Nilima Nigam (Simon Fraser University)
Naoki Saito (University of California at Davis)