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Department of

Mathematics

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Andrew Harder, assistant professor of mathematics at Lehigh University

Andrew Harder

Assistant Professor

610.758.4678
anh318@lehigh.edu
0017 - Chandler-Ullmann Hall
Education:

Ph.D., University of Alberta, 2016

M.Sc., Queen’s University, 2011

B.Sc., Queen’s University, 2009

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Additional Interests

  • Algebraic geometry
  • Hodge theory
  • Calabi-Yau varieties
  • Mathematical physics

Research Statement

Professor Harder studies algebraic geometry, using tools from Hodge theory and addressing mathematical problems with roots in physics. His Ph.D. thesis focused on applications of tools from mirror symmetry to classify Calabi-Yau threefold admitting K3 surface fibrations. His post doctoral work studied Landau-Ginzburg models, from categorical and Hodge theoretic perspectives. Currently, his work studies aspects of holomorphic symplectic geometry, tropical geometry, and their interactions with Hodge theory, as well as studying relationships between Feynman integrals and period functions of algebraic varieties.

Biography

Professor Harder received B.Sc. and M.Sc. degrees from Queen’s University at Kingston in 2009 and 2011 respectively. He obtained his Ph.D. from the University of Alberta in 2016, after which he was a research assistant professor at the University of Miami as part of the Simons Collaboration in Homological Mirror Symmetry. He joined the faculty at Lehigh University in January 2019.

Recent publications and preprints

1. Modularity of Landau--Ginzburg models, with Charles F. Doran, Ludmil Katzarkov, Victor Przyjalkowski, and Mikhail Ovcharenko, submitted.
2. Motivic geometry of 2-loop Feynman integrals, with Charles F. Doran, and Pierre Vanhove, submitted.
3. Mixed Hodge structures in log symplectic geometry, submitted.
4. Torus fibers and the weight filtration. To appear, Proceedings of the AMS.
5. P=W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds, with Zhiyuan Li, Junliang Shen, and Qizheng Yin. Forum of Mathematics, Sigma, 2021.
6. Hodge numbers of Landau--Ginzburg models. Advances in Mathematics, 2021.
7. P=W phenomena, with Ludmil Katzarkov and Victor Przyjalkowski. Mathematical Notes, 2021.
8. Pseudolattices, del Pezzo surfaces, and Lefschetz fibrations, with Alan Thompson. Transactions of the AMS, 2019.
9. Perverse sheaves of categories and some applications, with Ludmil Katzarkov. Advances in Mathematics, 2019.

Teaching

Spring 2023: Math 428, Fields and Modules.
Fall 2022: Math 023, Calculus III. Math 327, Groups and Rings.
Spring 2022: Math 450, Topics in Algebraic Geometry
Fall 2021:  Math 023, Calculus III. Math 327, Groups and Rings.
Spring 2021: Math 428, Fields and Modules
Fall 2020: Math 021, Calculus I. Math 327, Groups and Rings.
Spring 2020: Math. 450, Topics in Algebraic Geometry
Fall 2019: Math 021, Calculus I. Math 327, Groups and Rings.
Spring 2019: Math 023, Calculus III.