David P. Herzog

Assistant Professor

Dept. of Mathematics

Iowa State University

Office: Carver 474

Email: dherzog "at" iastate "dot" edu

CV

Iowa State Math Department Webpage

**Teaching (Fall '19)**

**Note**: All course materials can be found on Canvas.

**Research**

My main interests are in stochastic analysis, in particular stochastic differential equations. I also have interests in applied mathematics, and some of my research
in this area has been featured in popular press: DukeToday,
Pharmacy Times,
Futurity,
WUNC,
Healio,
ACSH, ICT, AHC Media. Currently, my research is supported in part by grants DMS-1612898 and DMS-1855504 from the National Science Foundation.

**Gamma calculus beyond Villani and explicit convergence estimates for Langevin dynamics with singular potentials** (PDF)

(F. Baudoin, M. Gordina, and D.P. Herzog). *Submitted*
**The generalized Langevin equation with a power-law memory in a nonlinear potential well** (PDF)

(N.E. Glatt-Holtz, D.P. Herzog, S.A. McKinley, and H.D. Nguyen). *Submitted*.
**Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials** (PDF)

(D.P. Herzog and J.C. Mattingly). *Comm. Pure Appl. Math. * **72** no. 10 pp. 2231-2255 (2019)
**Exponential relaxation of the Nosé-Hoover thermostat under Brownian heating** (PDF)

(D.P. Herzog). *Commun. Math. Sci.* **16** no. 8 pp. 2231-2260 (2018)
**Scaling and saturation in infinite-dimensional control problems with applications to SPDEs** (PDF)

(N.E. Glatt-Holtz, D.P. Herzog and J.C. Mattingly). *Annals of PDE* **4** no. 2 , 103 pages (2018).
**Geometric ergodicity of two-dimensional Hamiltonian systems with a Lennard-Jones-Like repulsive potential** (PDF)

(B. Cooke, D.P. Herzog, J.C. Mattingly, S.A. McKinley, S.C. Schmidler). *Commun. Math. Sci.* **15** no. 7 pp. 1987-2025 (2017).
**The small-mass limit for Langevin dynamics with unbounded coefficients and positive friction** (PDF)

(D.P. Herzog, S. Hottovy and G. Volpe). *J. Stat. Phys.* **163** no. 3 pp.659-673 (2016).
**Noise-induced stabilization of planar flows II** (PDF)

(D.P. Herzog and J.C. Mattingly). *Electron. J. Probab.* **20** no. 113 pp.1-37 (2015).
**Noise-induced stabilization of planar flows I** (PDF)

(D.P. Herzog and J.C. Mattingly). *Electron. J. Probab.* **20** no. 111 pp.1-43 (2015).
**A practical criterion for positivity of transition densities** (PDF)

(D.P. Herzog and J.C. Mattingly). *Nonlinearity* **28** pp.2823-2845 (2015).
**Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies** (PDF)

(M.D. Ryser, K. McGoff, D.P. Herzog, D.J. Sivakoff and E.R. Myers). *Epidemics* **11** pp.32-47 (2015).
**An extension of Hormander's hypoellipticity theorem** (Journal)

(D.P. Herzog and N. Totz). *Potential Anal.* **42** pp.403-433 (2015).
**The transition from ergodic to explosive behavior in a family of stochastic differential equations** (PDF)

(J. Birrell, D.P. Herzog and J. Wehr). *Stochastic Process. Appl.* **122** pp.1519-1539 (2012).
**Ergodic properties of a model for turbulent dispersion of inertial particles**
(PDF)

(K. Gawedzki, D.P. Herzog and J. Wehr).
*Comm. Math. Phys.* **308** pp.49-80 (2011).
**Geometry's fundamental role in the stability of stochastic differential equations** (PDF)

*Ph.D. Dissertation* (2011).