Current Position:

Associate professor, University of Arizona.

Previous Positions:

LE Dickson Instructor, University of Chicago (2016-2019)

LabEx MILYON post-doc, UMPA / ENS de Lyon (2015-2016)

Education:

Stanford University (2010-2015), Advisor: Lenya Ryzhik

Research:

Broadly my research is in applied analysis and partial differential equations for models arising in the physical, biological, and social sciences as well as engineering.

Funding (Current):
* NSF CAREER DMS-2337666, (2024-29)

* NSF DMS-2204615, (2022-2025)

1. A Hamilton-Jacobi approach to road-field reaction-diffusion models
   (with Lam) Submitted     

2. A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation
   (with Lucertini, Wang) Submitted     

3.       Decay estimates and continuation for the non-cutoff Boltzmann equation
   (with Snelson, Tarfulea) Submitted

4. Front location determines convergence rate to traveling waves
   (with An, Ryzhik) Ann. Inst. H. Poincaré Anal. Non Linéaire, accepted

5. Traveling waves for the Keller-Segel-FKPP equation with strong chemotaxis
   (with Rezek) J. Diff. Equations, 2024.

6. Speed-up of traveling waves by negative chemotaxis
   (with Griette, Turanova) J. Funct. Anal., 2023.

7. Voting models and semilinear parabolic equations
   (with An, Ryzhik) Nonlinearity, 2023.

8. Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts
   (with An, Ryzhik) Arch. Ration. Mech. Anal., 2023.

9. Classical solutions of the Boltzmann equation with irregular initial data
   (with Snelson, Tarfulea) Ann. Sci. Éc. Norm. Supér., to appear

10. Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation
    (with Wang) Discrete Contin. Dyn. Syst., 2024.

11. Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation
    (with An, Ryzhik) J. Eur. Math. Soc. (JEMS), to appear.

12. Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data
    (with Wang) SIAM J. Math. Anal., 2022.

13. Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis
    J. Math. Pures Appl., 2022.

14. Long-time behavior for a nonlocal model from directed polymers
    (with Gu) Nonlinearity, 2023.

15. The speed of traveling waves in a FKPP-Burgers system
    (with Bramburger) Arch. Ration. Mech. Anal., 2021.     [Code Repository]

16. The Bramson delay in a Fisher-KPP equation with log-singular nonlinearity
    (with Bouin) Nonlinear Anal., 2021.

17. Self-generating lower bounds and continuation for the Boltzmann equation
    (with Snelson, Tarfulea) Calc. Var. Partial Differential Equations, 2020.

18. A PDE hierarchy for directed polymers in random environments
    (with Gu) Nonlinearity, 2021.

19. Local well-posedness of the Boltzmann equation with polynomially decaying initial data
    (with Snelson, Tarfulea) Kinet. Relat. Models, 2020.

20. Local solutions of the Landau equation with rough, slowly decaying initial data
    (with Snelson, Tarfulea) Ann. Inst. H. Poincaré Anal. Non Linéaire, 2020.

21. Non-local competition slows down front acceleration during dispersal evolution
    (with Calvez, Mirrahimi, Turanova (and a numerical appendix by Dumont)) Ann. H. Lebesgue, 2022.

22. Brownian fluctuations of flame fronts with small random advection
    (with Souganidis) Math. Models Methods Appl. Sci., 2020.

23. Local existence, lower mass bounds, and a new continuation criterion for the Landau equation
    (with Snelson, Tarfulea) J Differential Equations, 2019

24. The Bramson delay in the non-local Fisher-KPP equation
    (with Bouin, Ryzhik) Ann. Inst. H. Poincaré Anal. Non Linéaire, 2019.

25. Propagation in a Fisher-KPP equation with non-local advection
    (with Hamel) J. Funct. Anal., 2020

26. C∞ smoothing for weak solutions of the inhomogeneous Landau equation
    (with Snelson) Arch. Ration. Mech. Anal, 2019

27. The reactive-telegraph equation and a related kinetic model
    (with Souganidis) NoDEA, 2017

28. Thin front limit of an integro--differential Fisher--KPP equation with fat--tailed kernel
    (with Bouin, Garnier, Patout) SIAM J. Math. Anal., 2018

29. Super-linear propagation for a general, local cane toads model
    (with Perthame, Souganidis) Interface Free Bound., 2018

30. Influence of a mortality trade-off on the spreading rate of cane toads fronts
    (with Bouin, Chan, Kim) Comm. Partial Differential Equations, 2018

31. The Bramson logarithmic delay in the cane toads equation
    (with Bouin, Ryzhik) Q. Appl. Math., 2017

32. Super-linear spreading in local bistable cane toads equations
    (with Bouin) Nonlinearity, 2017

33. Ricci curvature bounds for weakly interacting Markov chains
    (with Erbar, Menz, Tetali) Electron. J. Probab. 2017, 2017

34. Super-linear spreading in local and non-local cane toads equations
    (with Bouin, Ryzhik) J. Math. Pures Appl., 2017

35. Propagation of solutions to the Fisher-KPP equation with slowly decaying initial data
    Nonlinearity, 2016

36. Equivalence of a mixing condition and the LSI in spin systems with infinite range interaction
    (with Menz) Stoch. Proc. Appl., 2016

37. Stability of Vortex Solutions to an Extended Navier-Stokes System
    (with Gie, Iyer, Kavlie, Whitehead) Commun. Math. Sci., 2016

38. Population Stabilization in Branching Brownian Motion with Absorption
    Commun. Math. Sci., 2016

39. Pulsating Fronts in a 2D Reactive Boussinesq System
    Comm. Partial Differential Equations, 2014

40. Propagation Phenomena in Reaction-Advection-Diffusion Equations
    PhD Thesis (NOTE: All work presented in this thesis is now also contained in other published work)

All current teaching is handled through D2L, the University of Arizona's LMS. That said, as a student and researcher, I have often stumbled across notes of courses at other universities that were very helpful. Recently, however, it seems that notes are often only posted in (locked) LMS sites.

With this in mind, I have decided to start making my notes publicly available -- and encourage you to do so also! -- with the hopes they will be useful to someone somewhere. The come with the caveat that there may be typos, errors, etc, as they have not been carefully proofread.

• Math 584 -- Theoretical Foundations of Applied Mathematics

• Math 529 -- Special topics: Optimal transport and its applications

A long time ago (at the beginning of grad school), I wrote up a short proof that measurable functions that are additive on the rationals are additive on the reals. Since it has been referred to a few times on MathOverflow posts, I have been asked to continue hosting it. Here is it.