Picture of Axel;

Axel Saenz

University of Virginia, Mary Ann Pitts Postdoctoral Fellow.
UC Davis, Mathematics, PhD 2016.
Columbia University, Applied Math 2011.
Contact: ais6a at virginia dot edu

Research Interests:

Probability, Integrability, and Universality: I work on probability models with many particles that have weak interactions. This means that a single particle only interacts directly with its immediate neighbors and the accumulation of these local interactions govern the dynamics of the whole system in a non-trivial manner. In particular, when the number of particles increases, there are more local interactions that influence the global system and it makes the dynamics of the system highly complex. In general, one may not hope to "solve exactly" such complicated systems, but the exception are systems that are "integrable" (i.e. one may write explicit formulas describing the dynamics of the model). More importantly and somewhat surprising, when there are infinite number particles, it has been observed in the laboratory and in the calculations that the behaviour of integrable models is "universal" (under certain conditions) and this means that other models, which may not be solved exactly, behave very similar to an integrable model. This allows to solve for a wide class models by just solving one special model.
Specific Topics: Asymmetric Simple Exclusion Process (ASEP) on the ring, Schur processes, coordinate Bethe ansatz, Eynard-Orantin topological recursion. Painleve equations.
Check out some simulations on my YouTube Channel.


Department Probability Seminar.
Integrable Probability Seminar.


Integral formulas for ASEP and q-TAZRP on the ring , arXiv:1905.02987 (2019).
The KPZ universality class and related topics , arXiv:1904.03319 (2019).
Limiting speed of a second class particle in ASEP with Promit Ghosal and Ethan C. Zell, arXiv:1903.09615 (2019).
Generalizations of TASEP in discrete and continuous inhomogeneous space with Aliza Knizel and Leo Petrov, arXiv:1808.09855 (2018).
Painleve Equations, Topological Type Property and Reconstruction by the Topological Recursion with Kohei Iwaki and Olivier Marchal, arXiv:1601.02517v1 (2016).
The Completeness of the Bethe Ansatz for the Periodic ASEP, with Eric Brattain and Norman Do, arXiv:1511.03762v1 (2015).
Quantum Curve and the First Painleve Equation, with Kohei Iwaki, SIGMA 12 (2016), 011, 24 pages, arXiv:1507.06557v2 (2015).
My Dissertation: Integrability and tau-functions on Random Walkers & Isomonodromy Deformation Systems (June 2016)

Personal Info

I know how to swim.
My PhD adviser is Motohico Mulase.


Instructor at UVa:
    Spring: MATH 4110 (Introduction to Stochastic Processes)
    Spring 2019: MATH 3100 (Introduction to Probability)
    Fall 2018: MATH 3100 (Introduction to Probability)
    Spring 2018: MATH 3340 (Complex Variable with Applications)
    Fall 2017: MATH 3100 (Introduction to Probability)
    Summer 2017: MATH 3310 (Basic Real Analysis)
    Spring 2017: MATH 4110 (Introduction to Stochastic Processes)
    Fall 2016: MATH 3100 (Introduction to Probability)
    Fall 2016: MATH 4110 (Introduction to Stochastic Processes)
Instructor at UC Davis:
    Spring 2012: Math 16C (Calculus for Biology)
TA at UC Davis:
   Math 21B, 21C, 21D (Calculus for Engineering)

Departmental Service

Co-organizer for the Probability Seminar 2016-2019 (University of Virginia)
Co-organizer for the Seminar on Stochastic Processes 2017 (University of Virginia)
Galois Group President 2015-2016 (UC Davis).
Galois Group Vice President and Treasurer 2014-2015 (UC Davis).
Graduate Student Association departmental representative 2012-2013 (UC Davis).

Awards and Honors

2016: Kavli Institute for Theoretical Physics Graduate Fellow
2015-16: UC Davis Dissertation Year Fellowship
2014-15: UC Davis Graduate Research Mentorship Fellowship
2012-13: GAANN Fellowship