Department of Mathematics
New York, NY 10027
tpad [at] math [dot] columbia [dot] edu.
I am currently a Ritt Assistant Professor (postdoc) at Columbia University. From September 2020 to July 2021, I was a
member in the School of Mathematics at IAS. I received my Ph.D. at MIT in May 2020 under the supervision of Davesh Maulik, and my B.Sc. and M.A. from UCLA in June 2015.
I am interested in algebraic geometry, especially in noncommutative geometry (derived categories of coherent sheaves, matrix factorizations, noncommutative resolutions of singularities, and categorifications of constructions from cohomology, such as intersection cohomology) and in enumerative geometry (especially Donaldson-Thomas theory), and in geometric representation theory (Hall algebras and quantum groups).
- Calculus III in Fall 2022.
- Calculus II in Spring 2022.
- Calculus III in Fall 2021.
- Review of single and multivariable calculus (18.089) at MIT in Summer 2018 (with Kevin Sackel) and Summer 2019.
- The categorical DT/PT correspondence and quasi-BPS categories for local surfaces, joint with Y. Toda,
- The local categorical DT/PT correspondence, joint with Y. Toda,
- Categorical and K-theoretic Donaldson-Thomas theory of C3 (part II), joint with Y. Toda,
- Categorical and K-theoretic Donaldson-Thomas theory of C3 (part I), joint with Y. Toda,
- Relative stable pairs and a non-Calabi-Yau wall crossing, arXiv:2110.14561, Int. Math. Res. Not., DOI.
- Generators for K-theoretic Hall algebras of quivers with potential, arXiv:2108.07919, submitted.
- Categorical and K-theoretic Hall algebras for quivers with potential, arXiv:2107.13642, J. Inst. Math. Jussieu, DOI
- Generators for categorical Hall algebras of surfaces, arXiv:2106.05176, Math. Z. 303, 40 (2023).
- K-theoretic Hall algebras of quivers with potential as Hopf algebras, arXiv:2106.05169, Int. Math. Res. Not., DOI.
- Intersection K-theory, arXiv:2103.06223, submitted.
- Noncommutative resolutions and intersection cohomology for quotient singularities, arXiv:2103.06215, submitted.
- Deformed dimensional reduction, joint with B. Davison, arXiv:2001.03275, Geom. Topol. 26-2 (2022), 721-776.
- K-theoretic Hall algebras for quivers with potential, arXiv:1911.05526. This preprint is my PhD thesis. The articles "Generators for K-theoretic Hall algebras of quivers with potential" and "Categorical and K-theoretic Hall algebras for quivers with potential" are revised versions of material discussed in it.
- Groups of order p3 are mixed Tate, arXiv:1503.04235, to appear in Rend. Sem. Mat. Univ. Padova.
The next papers were written while I was a participant in the SMALL REU at Williams College:
- Ergodicity and conservativity of products of infinite transformation and their inverses, joint with J. Clancy, R. Friedberg, I. Kasmalkar, I. Loh, C.E.Silva, and S. Vasudevan, arXiv: 1408.2445, Colloq. Math. 143 (2016), no. 2, 271-291.
- On v-positive type transformation in infinite measure, joint with C.E.Silva and E. Zachos, arxiv:1309.6257,
Colloq. Math. 140 (2015), no. 2, 149-170.
- On rationally ergodic and rationally weakly mixing rank one transformations, joint with I. Dai, X. Garcia, and C.E.Silva, arXiv:1208.3161, Ergodic Theory Dynam. Systems 35 (2015), no. 4, 1141-1164.