Robert

Neel

# Curriculum Vitae

My CV is also available as a pdf. For links to some of the papers, please go to my research page.

Employment

- Lehigh University

Associate Professor, 2016-present.

Assistant Professor, 2009-2016. - Columbia University

NSF Postdoctoral Research Fellow, 2006-2009.

Ritt Assistant Professor, 2005-2006.

Education

- Harvard University, Ph.D. Mathematics,
June 2005.

Thesis: The behavior of the heat kernel at the cut locus.

Adviser: Daniel Stroock. - Stanford University, B.S. Mathematics
with honors and distinction (minor in Philosophy), June 1999.

Undergraduate Thesis Adviser: Robert Finn.

Papers

- A pseudo-probabilistic approach to the dilation equation for wavelets (with S. Dumnich), arXiv:1710.01364, preprint.
- Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group (with D. Barilari and U. Boscain), arXiv:1606.01159, to appear in Ann. Fac. Sci. Toulouse Math.
- Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling (with A. Agrachev, U. Boscain, and L. Rizzi), arXiv:1601.03304, to appear in ESAIM Control Optim. Calc. Var.
- Brownian motion and the parabolicity of minimal graphs, arXiv:0810.0669v1, currently-unpublished preprint.
- Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry (with U. Boscain and L. Rizzi), Adv. Math. 314 (2017), 124-184.
- On the heat diffusion for generic Riemannian and sub-Riemannian structures (with D. Barilari, U. Boscain, and G. Charlot), Int. Math. Res. Not. IMRN (2017), no. 15, 4639-4672.
- A stochastic target approach to Ricci flow on surfaces (with I. Popescu), Ann. Probab. 44 (2016), no. 2, 1341-1425.
- Martingales arising from minimal submanifolds and other geometric contexts, Illinois J. Math. 58 (2014), no. 2, 323-357. [actually published in 2015]
- Brownian motion and the Dirichlet problem at infinity on two-dimensional Cartan-Hadamard manifolds, Potential Anal. 41 (2014), no. 2, 443-462.
- On parabolicity and area growth of minimal surfaces, J. Geom. Anal. 23 (2013), no. 3, 1173-1188.
- Small-time heat kernel asymptotics at the sub-Riemannian cut locus (with D. Barilari and U. Boscain), J. Differential Geom. 92 (2012), no. 3, 373-416.
- Stochastic methods for minimal surfaces, Geometric analysis: partial differential equations and surfaces, Contemp. Math., vol. 570, Amer. Math. Soc., Providence, RI (2012), 111-136.
- A martingale approach to minimal surfaces, J. Funct. Anal. 256 (2009), no. 8, 2440-2472.
- The small-time asymptotics of the heat kernel at the cut locus, Comm. Anal. Geom. 15 (2007), no. 4, 845-890.
- Analysis of the cut locus via the heat kernel (with D. Stroock), Surveys in Differential Geometry, Vol. 9, International Press, Boston (2004), 337-349.
- Equilibrium configurations for a floating drop (with A. Elcrat and D. Siegel), J. Math. Fluid Mech. 6 (2004), no. 4, 405-429.
- C-singular solutions of the capillary problem (with R. Finn), J. Reine Angew. Math. 512 (1999), 1-25.

Awards

- Simons Foundation Collaboration Grant, 2017-present.
- NSA Mathematical Sciences Program research grant, "Martingale methods for geometric structures including minimal submanifolds, curvature flows, and sub-Riemannian manifolds," 2015-2017.
- Frank Hook Assistant Professorship, Lehigh University, 2014-2016.
- NSF Postdoctoral Research Fellowship, 2006-2009.
- Clay Mathematics Institute Liftoff Fellowship, 2005.
- Certificate of Distinction in Teaching, Harvard University, Fall 2002, Fall 2003, and Spring 2005.
- NSF Graduate Research Fellowship, 2000-2003.
- Fulbright Grant to study at the University of Leipzig, 1999-2000.

Talks

- 2018
- Workshop on Stochastic Systems: their Analysis, Geometry, and Perturbation, Chinese Academy of Sciences (Beijing) • Probability Seminar, University of Illinois
- 2017
- Conference "The last 60 years of Mathematical Fluid Mechanics," Vilnius University (Lithuania) • Conference ProbaGeo, University of Luxembourg • Geometry Seminar, University of Rochester • Differential Geometry Seminar, UC Irvine
- 2016
- Workshop on "Heat Kernels, Stochastic Processes and Functional Inequalities," Oberwolfach (Germany) • Mathematical Sciences Colloquium, Worcester Polytechnic Institute • Mathematics Lecture Series, Wichita State University
- 2015
- Probability and Mathematical Physics Seminar, NYU/Courant • Probability Seminar, University of Luxembourg • Analysis and Probability Seminar, University of Connecticut • Probability Seminar, Purdue University
- 2014
- Probability Seminar, University of Virginia • Workshop on geometric analysis on sub-Riemannian manifolds, Institut Henri Poincaré (France) • Conference ProbaGéo, University of Bordeaux (France) • Stochastics Seminar, Georgia Tech • Mathematical Finance and Probability Seminar, Rutgers University
- 2013
- Probability Seminar, University of Luxembourg • SIAM Conference on Control and Its Applications, San Diego • Geometric Analysis Seminar, Cornell University
- 2012
- Math Department Colloquium, Lehigh University • Probability Seminar, Cornell University • Probability Seminar, NYU/Courant • Stochastics Seminar, Georgia Tech
- 2011
- Probability/Geometry Seminar, UT-Austin • Geometric Analysis Seminar, MIT • Math Department Seminar, University of Padua (Italy) • Geometric Analysis Seminar, SISSA (Trieste, Italy) • CMAP Seminar, École Polytechnique (Paris, France)
- 2010
- Probability Seminar, UT-Austin • Probability Seminar, Cornell University • Math Department Colloquium, Purdue University • Santaló Summer School on Geometric Analysis, University of Granada (Spain)
- 2009
- Minimal Surfaces Arbeitsgemeinschaft, Oberwolfach (Germany) • Geometric Analysis Seminar, MIT • Math Department Colloquium, Lehigh University
- 2008
- Analysis and PDE Seminar, Johns Hopkins University • Geometry and Topology Seminar, University of Massachusetts at Amherst • Stochastics Seminar, Georgia Tech
- 2006
- Probability Seminar, NYU/Courant • Analysis and Geometry Seminar, Columbia University • Summer School: Probabilistic and Analytic Perspectives on Contemporary PDEs, Carnegie Mellon University • CUNY Differential Geometry Seminar • Columbia-Princeton Probability Day
- 2005
- Probability Seminar, Columbia University • Probability Seminar, Northwestern University
- 2004
- Stochastic Analysis Seminar, University of Illinois • Analysis Seminar, MIT

Teaching

Lehigh University- Math 463: Advanced Probability
- Math 402: Real Analysis II
- Math 401: Real Analysis I
- Math 309: Theory of Probability
- Math 301: Principles of Analysis I
- Math 295: Intro to Probability Theory
- Math 231: Probability and Statistics
- Math 205: Linear Methods
- Math 96/98: Calculus II, Part B and Differential Equations
- Math 23: Calculus III

- Math W4155: Probability Theory
- Math V2010: Linear Algebra
- Math V1202: Calculus IV
- Math V1201: Calculus III
- Math V1101: Calculus I

Advising

Doctoral students- Sarah Dumnich, graduated Spring 2016.

Service

Lehigh University- Chair of the math department's graduate committee/director of graduate studies, 2017-present.
- Undergraduate Mentor Advisor, 2017-present.
- Member of the College of Arts and Sciences nominations committee, 2015-2018.
- Member (elected by the department) of the chair's advisory committee for the math department, 2012-2013, 2014-2015 and 2016-2017.
- Member of the university's planning committee for the renovation of Christmas-Saucon Hall, 2015-2017.
- Member of the university's honorary degrees committee, 2014-2017.
- Member of the math department's calculus committee, 2012-2017.
- (Co-) organizer of math department's colloquium, 2010-2012 and 2014-2015.
- Member of the local organizing committee for the International Symposium on Geometry and Topology at Lehigh University, 2010.

- Grant proposal reviewer for (French) National Research Agency (ANR) and (Canadian) Natural Sciences and Engineering Research Council (NSERC).
- Reviewer for MathSciNet (Mathematical Reviews).
- Have refereed for Stochastic Processes and their Applications, Annals of Global Analysis and Geometry, ALEA, Journal of Theoretical Probability, Annales de l'Institut Fourier, Communications in Analysis and Geometry, Probability Theory and Related Fields, Journal of Differential Geometry, Potential Analysis, Electronic Journal of Probability, Mathematische Annalen, Journal für die reine und angewandte Mathematik (Crelle's journal), Mathematische Zeitschrift, Monatshefte für Mathematik, SIAM Journal on Financial Mathematics, Journal of Geometric Analysis, Geometria Dedicata, Journal of Differential Equations, and Journal of Functional Analysis.
- Mentor for Fulbright applicants through Stanford University's office of overseas studies, 2013-present.
- Member of the American Mathematical Society (AMS), 2011-present.
- Member of the organizing committee for the 31st Midwest Probability Colloquium (held at Northwestern University), 2008-2009.