- Modeling and analysis of active biological systems
- Mathematics of deep neural networks and machine learning
- Homogenization theory, multiscale analysis and continuum limits
- Nonlinear PDE/variational problems in Biology and Materials Science
- Random media and disordered materials
Ph.D. in Mathematics,
Kharkov State University, USSR, 1984.
Thesis: Homogenization of elasticity equations in domains with fine-grained boundaries.
Advisor: E. Khruslov, member of National Academy of Science, Ukraine
- Honorary Professor (Professoris Honoris Causa) of the Moscow State University "for his important contribution to Applied Mathematics and Mathematical Physics" (2017)
C.I. Noll Award for excellence in teaching, Penn State University (2004)
Annual recognition of an outstanding faculty member in the Eberly College of Science
- The PI on NIH (National Institute of Health) RO1 grant "Collaborative Research: Predictive modeling of collective swimming in bacterial suspensions" (2012-2017).
- My research also has been funded by NSF (programs: Applied Mathematics, Physics of Living Systems, and Design of Materials to Revolutionze and Engineer our Future), DOE (US Department of Energy), and private industry.
- Author of about 100 refereed publications and two books.
Two publications in Scientific Reports: Nature Publishing Group (2013, 2015), senior author on both publications
- Professor of Mathematics, Department of Mathematics, PSU
- Member of The Materials Research Institute, PSU
- Member of The Huck Institute of Life Sciences, PSU
ADMINISTRATIVE DUTIES AT PSU:
- One of the two co-Directors of PSU Center for Mathematics of Living and Mimetic Matter.
- One of the two co-Directors of PSU Center for Interdisciplinary Mathematics.
- Member of advisory board of The Huck Institute of Life Sciences (Kitchen cabinet)
LONG-TERM VISITING POSITIONS:
- Spring 2016: Max-Planck Institute for Mathematics in the Sciences, Germany
- Spring 2016: Renmin University/Jiao Tong Univeristy, China
- Fall 2015: Sorbonne University, Paris 6, J.-L. Lions Lab, France
- Fall 2015: Argonne National Lab
- Spring 2009: Argonne National Lab
- Spring 2009: University of Lyon 1, France
- Fall 2008: Max-Planck Institute for Mathematics in the Sciences, Germany
- Fall 2008: Sarbonne University, Paris 6, J.-L. Lions Lab, France
- Fall 2008: University of Chicago
- Spring 2002: California Institute of Technology, Pasadena, California
- Spring 2002: Los Alamos National Lab, Los Alamos, New Mexico
- Fall 2001: Sarbonne University, Paris 6, J.-L. Lions Lab, France
- Fall 1996: Princeton University, Princeton, New Jersey
- Spring 1996: IMA (Institute for Mathematics and Applications), University of Minnesota, Minneapolis, Minnesota
- Spring 1991: IMA, University of Minnesota, Minneapolis, Minnesota
ADVISING GRADUATE STUDENTS/POSTDOCS:Total number of graduate students supervised (both Ph.D. and M.S.): 18.
Total number of postdoctoral fellows mentored: 11.
All former Ph.D. students are holding positions at major research Universities and US National Labs.
TEACHING EXPERIENCE:Teaching at The Pennsylvania State University since 1991. Undergraduate courses ranging from elementary through advanced levels.
Coordinator for a sophomore multi-section course "Ordinary Differential Equations".
Chair of the mid-term committee for Freshman Calculus (52 sections).
Coordinator for a sophomore multi-section course "Ordinary and Partial Differential Equations".
Graduate courses taught include: "Methods of Homogenization Theory in Mechanics of Composite Materials", "Percolation Theory and Its Applications", "Probability Theory", "Classical Mechanics and Calculus of Variations", "Multiscale Modeling and Applications in Biology", "Continuum Mechanics", "Homogenization Theory and Multiscale Analysis".
In charge of administering summer industrial internships for graduate students 1998 - present.
- 1993 - present: Society of Industrial and Applied Mathematics
- 2012 - present: Society of Mathematical Biology
- Managing Editor of Networks and Heterogeneous Media (2013 - present)
- Associate Editor of SIAM/ASA Journal on Uncertainty Quantification (2013 - 2016)
- Member of Editorial board of International Journal for Multiscale Computational Engineering (2003 - present)
- "On the convergence of formally diverging neural net-based classifiers” (with P.-E. Jabin), Comptes Rendus Mathematique, 356(4), 395-405 (2018), pdf.
- "Bifurcation of traveling waves in a Keller-Segel type free boundary model of cell motility” (with J. Fuhrmann, V. Rybalko), accepted to Communications in Mathematical Sciences, (2018), pdf.
- "A two scale Gamma-convergence approach for random non-convex homogenization" (with E. Sandier and S. Serfaty), Journal of Calculus of Variations and PDEs No. 6, p. 156 (2017), pdf.
- "Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit" (with M. Potomkin and V. Rybalko), Comptes Rendus Mathematique, 354(10), pp. 986-992 (2016), pdf.
- "Rayleigh Approximation for ground states of the Bose and Coulomb glasses" (with S. D. Ryan, V. Mityushev, and V. M. Vinokur), Scientific Reports: Nature Publishing Group, 5, 7821 (2015), pdf.
- "Flexibility of bacterial flagella in external shear results in complex swimming trajectories" (with M. Tournus, A. Kirshtein, and I. Aranson), Journal of the Royal Society Interface 12 (102) (2014), pdf.
- "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013), pdf.
- "Effective viscosity of bacterial suspensions: A three-dimensional PDE model with stochastic torque" (with B.M. Haines, I.S. Aranson, D.A. Karpeev), Comm. Pure Appl. Anal., v. 11(1), pp. 19-46 (2012), pdf.
- "Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast" (with H. Owhadi), Arch. Rat. Mech. Anal. , v. 198, n. 2, pp. 677-721 (2010), pdf.
- "Solutions with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg-Landau Equation" (with V. Rybalko), J. European Math. Society v. 12 n. 6, pp.1497-1531 (2009), pdf.
- "Fictitious Fluid Approach and Anomalous Blow-up of the Dissipation Rate in a 2D Model of Concentrated Suspensions" (with Y. Gorb and A. Novikov), Arch. Rat. Mech. Anal., v. 193, n. 3, pp. 585-622, (2009), DOI:10.1007/s00205-008-0152-2, pdf.
- "Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model" (with B. Haines, I. Aronson, and D. Karpeev), Physical Biology, 5:4, 046003 (9pp) (2008), pdf.
- "Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices" (with P. Mironescu), J. Functional Analysis, v. 239, n. 1, pp. 76-99 (2006), pdf.
- "Network Approximation in the Limit of Small Interparticle Distance of the Effective Properties of a High-Contrast Random Dispersed Composite" (with A. Kolpakov), Archive for Rational Mechanics and Analysis, 159, pp. 179-227 (2001), pdf.
- "Non-Gaussian Limiting Behavior of the Percolation Threshold in a Large System" (with J.Wehr), Communications in Mathematical Physics, 185, 73-92 (1997), pdf.
- "Large Time Asymptotics of Solutions to a Model Combustion System with Critical Nonlinearity" (with J. Xin), Nonlinearity, 8:161-178 (1995), pdf.
- "Asymptotics of the Homogenized Moduli for the Elastic Chess-Board Composite" (with S. Kozlov), Archive for Rational Mechanics and Analysis, 118, 95-112 (1992), pdf.
- "Getting Acquainted with Homogenization and Multiscale" (with V. Rybalko), Birkhauser series Compact Textbooks in Mathematics, Springer (2018).
- "Introduction to Network Approximation for Materials Modeling" (with A. Kolpakov and A. Novikov), Cambridge University Press (2012), pdf.
SELECTED INVITED CONFERENCE TALKS IN RECENT 5 YEARS:
- May 2019: Invited speaker at International workshop "Recent advances in Phase-Field modeling: from Engineering to Biology", Pavia, Italy.
- January 2019: Invited speaker at International workshop "18th-GAMM-Seminar on Microstructures", Berlin, Germany.
- January 2019: Invited speaker at International workshop "Surface, Bulk, and Geometric Partial DifferentialEquations: Interfacial, stochastic, non-local and discrete structures", Oberwolfach, Germany.
- July 2018: Invited speaker at NSF-SIAM Minisymposium on the NSF DMREF Program, Portland OR
- January 2018: Invited speaker at the IMA Workshop "Liquid Crystals, Soft-matter Packing, and Active Systems: Materials and Biological Applications", Minneapolis
- January 2018: Invited speaker at the workshop "Multiscale Problems in Materials Science and Biology: Analysis and Computation", Tsinghua Sanya International Mathematics Forum, China
- June 2017: Invited Plenary Speaker at the 5th International Conference "Analysis and Mathematical Physics" dedicated to Vladimir A. Marchenko's 95th birthday, Kharkiv, Ukraine
- September 2014: Invited lecture at summer workshop for students, "Getting started with PDE", Technion, Israel
- May 2014: Invited plenary speaker at the International conference "Multiscale Problems in Physics, Biology and Materials Science". Shanghai Jiao Tong University China
- March 2014: Invited plenary speaker at International School "Around Vortices: from Continuum to Quantum Mechanics". National Institute for Pure and Applied Mathematics (IMPA) Rio de Janeiro, Brazil
- October 2013: Invited plenary speaker at the International conference "PDEs and Dynamical Systems in Biology" Bar-Ilan University, Israel
- July 2013: Invited principal speaker at the International workshop "Workshop on "Quantized vortices in superfluidity and superconductivity and related problems" Wolfgang Pauli Institute (WPI), Vienna