Dr. César Arturo Garza
Biography
After earning my B.S. in Mechatronics Engineering, I entered the Masters in Mathematics program at UTEP with Dr. Luis Valdez-Sanchez as my advisor. We worked on hyperbolic knots and Dehn surgeries. In 2009, I entered the doctoral program at UT Austin under the supervision of Dr. Andrew Neitzke. I worked on the construction of hyperkahler metrics on certain Hitchin systems. For 2015-2017, I was a Postdoctoral Researcher at IUPUI sponsored by Dr. Alexander Its, working on the Riemann-Hilbert problem and their applications in Geometry.
Degrees Earned
Ph.D. in Mathematics, University of Texas
M.S. in Mathematics, UTEP
Courses Taught
MATH 1301: College Algebra
MATH 2401: Calculus I
Experience Qualifications
2015-2017: Postdoctoral Researcher, Indiana University-Perdue University Indianapolis
2017-present: Assistant Professor, University of Houston-Downtown
More Information
Academic Interests
I'm interested in applications of Riemann-Hilbert problems in Complex Geometry. In particular, certain complex integrable systems arising from the study of moduli spaces of Higgs bundles have a very rich geometry. These are hyperkahler manifolds and in certain cases, it is possible to obtain the hyperkahler metric through solutions of an infinite-dimensional Riemann-Hilbert problem.
I also study the analytic aspects of the Riemann-Hilbert problems and their relation to canonical factorization, state space realizations and isomonodromic deformations from a geometrical perspective.
Publications
2017: A construction of hyperkähler metrics through Riemann-Hilbert problems I (submitted)
2017: A construction of hyperkähler metrics through Riemann-Hilbert problems II (submitted)
Award
2016, 2015: IUPUI Athletics Favorite Professor