Felix Janda

Assistant Professor at the University of Illinois Urbana-Champaign
Adjunct Professor at the University of Notre Dame
CV
PhD thesis (under R. Pandharipande at ETH Zürich)
ORCID Google Scholar

Contact information

Felix Janda
University of Illinois Urbana-Champaign
303 Altgeld Hall
Urbana, IL 61801
USA
Email: fjanda@illinois.edu

Teaching

Fall 2023: MATH 347: Fundamental Mathematics

Graduate Students

Nawaz Sultani (2019-2022), now postdoc at Academia Sinica, Taipei

Activities

Nov 2022: NSF Workshop on matrix factorizations and related topics
Feb 2019: FRG Workshop on strata of abelian differentials and related topics
Jan 2019: Workshop on Modular structures in Gromov-Witten theory and related topics
June 2017: RTG/FRG Mirror Symmetry Conference for Young Researchers
April 2017: FRG Special Lecture and Workshop
Jan 2017: RTG Workshop on Witten's r-spin class and related topics

Research

My general research area is moduli spaces in algebraic geometry. I study moduli spaces of curves, maps and related ones with applications to Gromov-Witten theory and strata of holomorphic differentials. During my PhD, my main focus has been on the study of tautological classes on the moduli space of curves. My current focus is on developing the geometric technique of "log GLSM", and to study its applications.

Publications/Preprints

All of my articles are available on the arXiv.
"Gromov-Witten Invariants of Non-Convex Complete Intersections in Weighted Projective Stacks" (with Nawaz Sultani and Yang Zhou), in preparation
"Structure results for torus fixed loci" (with Jarod Alper), in preparation
"Gromov-Witten invariants with naive tangency conditions" (with Tony Yue Yu), in preparation
"Punctured Logarithmic R-maps" (with Qile Chen and Yongbin Ruan) submitted, arXiv:2208.04519
"A comparison of group testing architectures for COVID-19 testing" (with Joshua Batson, Yaim Cooper, Nathaniel Bottman) , arXiv:2005.03051
"Virtual cycles of stable (quasi-)maps with fields" (with Qile Chen and Rachel Webb) in "Advances in Math" Volume 385, 16 July 2021, Art. No. 107781, 49pp, arXiv:1911.09825
"The logarithmic gauged linear sigma model" (with Qile Chen and Yongbin Ruan) in "Inventiones mathematicae", 225(3), 1077-1154, arXiv:1906.04345
"Structure of Higher Genus Gromov-Witten invariants of Quintic 3-folds" (with Shuai Guo and Yongbin Ruan) , arXiv:1812.11908
"Double ramification cycles with target varieties" (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine) in "Topology" Volume 13 Issue 4, December 2020, Pages 1725--1766, arXiv:1812.10136
"Towards Logarithmic GLSM: The $r$-spin case" (with Qile Chen, Yongbin Ruan and Adrien Sauvaget) accepted by Geometry and Topology, arXiv:1805.02304
"A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds" (with Shuai Guo and Yongbin Ruan) , arXiv:1709.07392
"Higher-genus wall-crossing in the gauged linear sigma model" (with Emily Clader and Yongbin Ruan) in "Duke Mathematical Journal" 170 (4), 697-773, (15 March 2021), arXiv:1706.05038
"Topological recursion relations from Pixton's formula" (with Emily Clader, Xin Wang and Dmitry Zakharov) accepted at Michigan Math Journal, arXiv:1704.02011
"Higher-genus quasimap wall-crossing via localization" (with Emily Clader and Yongbin Ruan) submitted, arXiv:1702.03427
"Appendix on the class of the locus of holomorphic differentials" (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine) in "Tautological relations via r-spin structures" by Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine in "Journal of Algebraic Geometry" 28 (2019), 439--496, arXiv:1607.00978
"Powers of the theta divisor and relations in the tautological ring" (with Emily Clader, Samuel Grushevsky and Dmitry Zakharov) in "International Mathematics Research Notices" Volume 2018 Issue 24, 12 December 2018, Pages 7725--7754, arXiv:1605.05425
"Double ramification cycles on the moduli space of curves" (with Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine) in "Publications de l'IHES" 125 (2017), 221--266, arXiv:1602.04705
"Pixton's double ramification cycle relations" (with Emily Clader) in "Geometry and Topology" 22-2 (2018), 1069--1108, arXiv:1601.02871
"Relations on $\overline M_{g,n}$ via equivariant Gromov-Witten theory of $\mathbb P^1$" in "Algebraic Geometry" (Foundation Compositio Mathematica) Volume 4, Issue 3 (May 2017), 311--336, arXiv:1509.08421
"Appendix: The weighted fundamental class of $\widetilde{\mathcal H}_g(\mu)$" (with Rahul Pandharipande, Aaron Pixton and Dimitir Zvonkine) in "The moduli space of twisted canonical divisors" by Gavril Farkas and Rahul Pandharipande in "Journal of the Institute of Mathematics of Jussieu" Volume 17, Issue 3 (June 2019), 615--672, arXiv:1508.07940
"Frobenius Manifolds near the Discriminant and Relations in the Tautological Ring" part of thesis, in "Letters in Mathematical Physics" 108 (2018), no 7, 1649--1675, arXiv:1505.03419
"The hypergeometric functions of the Faber-Zagier and Pixton relations" (with Alexandr Buryak and Rahul Pandharipande) in Pure and Applied Mathematics Quarterly Volume 11 (2015), Number 4 (Special volume dedicated to Prof. Eduard Looijenga), 591--631, arXiv:1502.05150
"Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures" part of thesis, not submitted, arXiv:1407.4778
"Gromov-Witten theory of target curves and the tautological ring" in Michigan Mathematical Journal, Volume 66, Issue 4 (2017), (683--698), arXiv:1308.6182
"Tautological relations in moduli spaces of weighted pointed curves" part of thesis, not submitted, arXiv:1306.6580
"Socle pairings on tautological rings" (with Aaron Pixton) in Epijournal de Géométrie Algébrique, Volume 3 (2019), Article no. 4, arXiv:1304.0026
"Gaussian rational points on a singular cubic surface" (with Ulrich Derenthal) in "Torsors, étale homotopy and applications to rational points", LMS Lecture Notes 405, Cambridge University Press, Cambridge, 2013, pp. 210-231, arXiv:1105.2807

My research has been supported by NSF grants DMS-1901748, DMS-2054830 and DMS-2239320.