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Andreas Malmendier

Assistant Professor
Department of Mathematics and Statistics
Utah State University
3900 Old Main Hill
Logan, UT 84322

USU Faculty Webpage
Office: Animal Science (ANSC) 307
Phone: (435) 797-5518
E-mail: andreas.malmendier[at]usu.edu

Research Interests:
Algebraic geometry, string theory, gauge theory

Grant Support:
Simons Collaboration Grant (2019-2024)
NSA Conference Grant (2018)
USU Research Catalyst Grant (2017)

Editorial Work:
Action Editor, Mathematical Physics: Experimental Results, Cambridge University Press


Organized Conferences

NSA Conference on Explicit Methods for Abelian and K3 Varieties, July 5-7 2019, USU, Logan
35th Jim Isenberg Pacific Coast Gravity Meeting, March 29-30 2019, USU, Logan
AMS Special Session Higher Genus Curves in Mathematical Physics and Arithmetic Geometry, January 6-9, 2016, Seattle
CMS Special Session on Fibrations, Mirror Symmetry and Calabi-Yau Geometry, December 5-6 2015, Montreal
AMS Special Session on Arithmetic of Algebraic Curves, March 22-23, 2014, Knoxville
String-Math 2014, June 9-13 2014, University of Alberta, Edmonton


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Other Publications

[27]  MIT, Ph.D. thesis in Mathematics
Expressions for the generating function of the Donaldson invariants of CP^2
Andreas Malmendier
Journal ref: Thesis (Ph.D.)-Massachusetts Institute of Technology. 2007. ProQuest LLC, Ann Arbor, MI.

The Donaldson invariants for CP^2 were obtained as the u-plane integral from an N=2 supersymmetric topological U(1)-gauge theory by Moore and Witten. We derive the generating function for the Donaldson invariants of CP^2 as the stationary phase approximation of the low-energy effective U(1)-gauge theory on CP^2 whereby obtaining an interpretation of the u-plane integral in terms of determinant line bundles. For the product of the determinant line bundles, the local and global anomalies vanish. Moreover, the product has a canonical trivialization. We show that the u-plane integral also arises as the stationary phase approximation of a heterortic sigma-model on an elliptic curve at the boundary of the Coulomb branch. The semi-classical generating function is described in terms of determinant line bundles on the Coulomb branch. We show that in terms of this generating function, the blow-up function for the Donaldson invariants derived by Fintushel and Stern arises in a natural way.


[28]  Universität Bonn, Diplom thesis in Physics
Geometrische Untersuchungen einer K3-Fläche aus dem Blickfeld der Stringtheorie [German]
Andreas Malmendier
Journal ref: Thesis (Diplom)-Rheinische Friedrich-Wilhelms-Universität Bonn. 2001. BONN-IR-2000-13.

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation. We construct approximations for the eigenfunctions and their asymptotic scattering phases with the help of the Liouville-Green approximation (WKB).


[29]  Praxis der Naturwissenschaften - Physik in der Schule [pdf]
Relativitätstheorie auf dem Homecomputer [German]
Andreas Malmendier, Tilman Enss
Journal ref: Praxis der Naturwissenschaften - Physik in der Schule, 35 (1997), no. 1, 30-33.

We describe the mathematical foundation and the development of our software visualizing several scenarios under the influence of special relativity. The effects include Lorentz contraction, Doppler shift, and less well known optical aberrations due to varying transit times of the travelling light rays.


Media Coverage: talks and interviews

USU Office of Research: Undergraduate Research Mentors of the Year, 2020
USU College of Science: Faculty Undergraduate Research Mentor of the Year, 2020
UnDisciplined: The Community Ecologist And The Mathematical Physicist, 2019
USU Today: In Pursuit of Everything, USU Mathematicians Share Findings, 2019
Elliptic fibrations on K3 surfaces with large Picard rank, 2018
Two-isogeny on Kummer surfaces, 2016
Multi-parameter families of K3 surfaces and hypergeometric functions, 2013
Heterotic/F-theory duality and lattice polarized K3 surfaces, 2013
New heterotic string vacua from pencils of genus-two curves, 2013
Heterotic/F-theory duality and lattice polarized K3 surfaces, 2011
How Einstein Invented GPS: Andreas Malmendier at TEDxColbyCollege, 2013


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