237A Illini Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
I was born in California and grew up in Houston and Mexico City. I got my undergraduate degree in applied mathematics and worked in financial risk management in Mexico before getting my PhD under Rafe Mazzeo at Stanford. I did postdocs at MIT, NYU/IAS, and Paris before coming to UIUC in 2011.
My research is in geometric analysis. I am particularly interested in analytic representations of topological invariants, analysis on non-compact or singular spaces, spectral geometry, heat kernels, and Dirac operators.
PhD Mathematics, Stanford, 2005
Albin, P., Rochon, F., & Sher, D. (2021). Resolvent, heat kernel, and torsion under degeneration to fibered cusps. Memoirs of the American Mathematical Society, 269(1314), 1-138. https://doi.org/10.1090/memo/1314
Albin, P. (2020). Poincaré-Lovelock metrics on conformally compact manifolds. Advances in Mathematics, 367, . https://doi.org/10.1016/j.aim.2020.107108
Albin, P., Rochon, F., & Sher, D. (2018). Analytic torsion and R-torsion of Witt representations on manifolds with cusps. Duke Mathematical Journal, 167(10), 1883-1950. https://doi.org/10.1215/00127094-2018-0009
Albin, P., Leichtnam, E., Mazzeo, R., & Piazza, P. (2018). Hodge theory on Cheeger spaces. Journal fur die Reine und Angewandte Mathematik, 2018(744), 29-102. https://doi.org/10.1515/crelle-2015-0095
Albin, P. (2017). On the Hodge theory of stratified spaces. In Hodge theory and L2-analysis (Vol. 39, pp. 1-78). (Adv. Lect. Math. (ALM)). Int. Press, Somerville, MA.