Leonid Berlyand is a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

and American mathematician, a professor of

Penn State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsyl ...

. He is known for his works on

homogenization Homogeneity is a sameness of constituent structure. Homogeneity, homogeneous, or homogenization may also refer to: In mathematics * Asymptotic homogenization, a method to study partial differential equations with highly oscillatory coefficients ...

Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomen ...

, mathematical modeling of

active matter Active matter is matter composed of large numbers of active "agents", each of which consumes energy in order to move or to exert mechanical forces. Such systems are intrinsically out of thermal equilibrium. Unlike thermal systems relaxing toward ...

and mathematical foundations of

deep learning Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience a ...

Life and career

Berlyand was born in

Kharkov Kharkiv, also known as Kharkov, is the second-largest List of cities in Ukraine, city in Ukraine.

on September 20, 1957. His father, Viktor Berlyand, was a mechanical engineer, and his mother, Mayya Genkina, an electronics engineer. Upon his graduation in 1979 from the department of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and

mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...

at the National University of Kharkov, he began his doctoral studies at the same university and earned a Ph.D. in 1984. His Ph. D. thesis studied the homogenization of elasticity problems. He worked at the Semenov Institute of Chemical Physics in

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

. In 1991 he moved to the United States and started working at

Pennsylvania State University The Pennsylvania State University (Penn State or PSU) is a Public university, public Commonwealth System of Higher Education, state-related Land-grant university, land-grant research university with campuses and facilities throughout Pennsyl ...

, where he has served as a full professor since 2003. He has held long-term visiting positions at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

, the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

, the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

, the

Max Planck Institute for Mathematics in the Sciences The Max Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig is a research institute of the Max Planck Society. Founded on March 1, 1996, the institute works on projects which apply mathematics in various areas of natural science ...

, Argonne and Los Alamos National Laboratories. His research has drawn support from the

National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

(NSF),

NIH The National Institutes of Health (NIH) is the primary agency of the United States government responsible for biomedical and public health research. It was founded in 1887 and is part of the United States Department of Health and Human Service ...

NIGMS The National Institute of General Medical Sciences (NIGMS) is one of the National Institutes of Health (NIH), the principal medical research agency of the United States Federal Government. NIH is a component of the U.S. Department of Health a ...

, the

Applied Mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

Program of the DOE Office of Sciences, BSF (the Bi-National Science Foundation USA-Israel) and the

NATO The North Atlantic Treaty Organization (NATO ; , OTAN), also called the North Atlantic Alliance, is an intergovernmental organization, intergovernmental Transnationalism, transnational military alliance of 32 Member states of NATO, member s ...

Science for Peace and Security Section. Berlyand has authored roughly 100 works on homogenization theory and PDE/ variational problems in

biology Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and ...

and

material science A material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their geol ...

. He has organized a number of professional conferences and serves as a co-director of the Center for Mathematics of Living and Mimetic Matter at

. He has supervised 17 graduate students and ten postdoctoral fellows.

Research

Drawing upon fundamental works in classical homogenization theory, Berlyand advanced the methods of homogenization in many versatile applications. He obtained mathematical results applicable to diverse scientific areas including biology,

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

, and

. His

mathematical modeling A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...

explains striking experimental result in the collective swimming of

bacteria Bacteria (; : bacterium) are ubiquitous, mostly free-living organisms often consisting of one Cell (biology), biological cell. They constitute a large domain (biology), domain of Prokaryote, prokaryotic microorganisms. Typically a few micr ...

. His homogenization approach to multi-scale problems was transformed into a practical computational tool by introducing a concept of polyharmonic homogenization which led to a new type of multiscale

finite elements Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

. Together with H. Owhadi, he introduced a "transfer-of-approximation" modeling concept, based on the similarity of the asymptotic behavior of the errors of Galerkin solutions for two elliptic PDEs. He also contributed to mathematical aspects of the

superfluidity Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...

by introducing a new class of semi-stiff boundary problems.

Awards and honors

* C. I. Noll Award for Excellence in Teaching, Penn State University (2004). *

Honorary professor Honorary titles (professor, president, reader, lecturer) in academia may be conferred on persons in recognition of contributions by a non-employee or by an employee beyond regular duties. This practice primarily exists in the UK and Germany, as ...

of the

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

"''for his important contribution to Applied Mathematics and Mathematical Physics''" (2017) *

Humboldt Prize The Humboldt Research Award (), also known informally as the Humboldt Prize, is an award given by the Alexander von Humboldt Foundation of Germany to internationally renowned scientists and scholars who work outside of Germany in recognition of ...

(2021)

Membership in professional associations

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...

(since 1993) *

Society for Mathematical Biology The Society for Mathematical Biology (SMB) is an international association co-founded in 1972 in the United States by George Karreman, Herbert Daniel Landahl and (initially chaired) by Anthony Bartholomay for the furtherance of joint scientific ac ...

(since 2012)

Editorship

* Managing Editor of Networks and Heterogeneous Media * Associate Editor of SIAM/ASA Journal on Uncertainty Quantification (2013–2016) * Member of Editorial board of International Journal for Multiscale Computational EngineeringBerlyand in the list of the Editorial Board of the International Journal for Multiscale Computational Engineering
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Books (author)

* "Introduction to Network Approximation for Materials Modeling" (with A. Kolpakov and A. Novikov), Cambridge University Press, 2012. * "Getting Acquainted with Homogenization and Multiscale" (with V. Rybalko), part of the Compact Textbooks in Mathematics book series, Springer, 2018. * "Mathematics of Deep Learning. An Introduction" (with P.-E. Jabin) De Gruyter, In the series De Gruyter Textbook, 2023.

Selected publications

* "Stability in the Training of Deep Neural Networks and Other Classifiers" (with P.-E. Jabin and C. A. Safsten), Mathematical Models and Methods in Applied Sciences (M3AS)}, v. 31(11), pp. 2345-2390 (2021

* "Phase-Field Model of Cell Motility: Traveling Waves and Sharp Interface Limit" (with M. Potomkin and V. Rybalko), Comptes Rendus Mathématique, 354(10), pp. 986–992 (2016

* "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

* "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

* "Vortex phase separation in mesoscopic superconductors" (with O. Iaroshenko, V. Rybalko, V. M. Vinokur), Scientific Reports: Nature Publishing Group 3 (2013

* "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

* "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

* "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

* "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-

* "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

* "Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices" (with P. Mironescu), Journal of Functional Analysis, v. 239, n. 1, pp. 76–99 (2006

* "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

* "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

* "Asymptotics of the Homogenized Moduli for the Elastic Chess-Board Composite" (with S. Kozlov), Archive for Rational Mechanics and Analysis, 118, 95–112 (1992

References

External links

Berlyand's page at the site of the Penn State University

Press release of Berlyand's research on Coulomb glasses

A conference in honor of Leonid Berlyand's 60th birthday
{{DEFAULTSORT:Berlyand, Leonid 1957 births Living people American mathematicians Mathematicians from Pennsylvania Soviet mathematicians Partial differential equation theorists Mathematical physicists National University of Kharkiv alumni Pennsylvania State University faculty People from State College, Pennsylvania Humboldt Research Award recipients