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Arul ShankarView profile

Professor

• Number Theory
• Arithmetic Statistics
• Elliptic Curves
• +3 more

Arul Shankar is a Professor of Mathematics at the University of Toronto, with his primary appointment at the Mississauga campus (UTM). He holds an office at 215 Huron Street, Room 1023 and can be reached at ashankar@math.utoronto.ca. His research focuses on Number Theory and Arithmetic Statistics, with particular expertise in elliptic curves, Selmer groups, and class groups. Professor Shankar's research interests center on the arithmetic statistics of number fields and elliptic curves. His work has significantly advanced our understanding of the average rank of elliptic curves, the distribution of Selmer groups, and the statistics of class groups. He has developed innovative applications of the geometry of numbers to arithmetic problems, often in collaboration with Manjul Bhargava and other leading number theorists. His research bridges deep theoretical questions with statistical approaches to understand the behavior of arithmetic objects across families. His publications reveal a consistent focus on the statistical behavior of arithmetic invariants, with particular attention to bounding average ranks of elliptic curves and understanding the distribution of class groups. The work demonstrates sophisticated applications of geometry of numbers techniques to problems in arithmetic statistics, with results published in top journals including the Annals of Mathematics, Inventiones Mathematicae, and Journal of the American Mathematical Society. Scientific Awards: 2018 Sloan Research Fellowship from the Alfred P. Sloan Foundation Professor Shankar is currently on sabbatical as a Simons Fellow. His research has established foundational results in arithmetic statistics, particularly regarding the average rank of elliptic curves and the distribution of class groups across families of number fields. His work with Bhargava on bounding the average rank of elliptic curves represented a major breakthrough in the field. His research group focuses on extending geometry of numbers methods to new contexts in arithmetic statistics, with recent work examining coregular vector spaces and applications to class groups. The lab maintains strong collaborations with number theorists at leading institutions worldwide.

Francesco SicaView profile

Assistant Professor

• Public-key cryptography
• Mathematical cryptology
• Number Theory
• +2 more

Francesco Sica is an Assistant Professor in the Department of Mathematics and Statistics at Florida Atlantic University, with research focused on mathematical cryptology, public-key cryptography, and number theory. He earned his Ph.D. in Mathematics from McGill University (1998), M.Sc. from Scuola Normale Superiore (1993), and B.Sc. from the University of Pisa (1993). Education Ph.D. in Mathematics, McGill University, Canada (1998) M.Sc. in Mathematics, Scuola Normale Superiore, Italy (1993) B.Sc. in Mathematics, University of Pisa, Italy (1993) His research spans implementation and security analysis of elliptic curve cryptography , including isogeny-based problems and torsion point attacks. He has also contributed to pseudorandom number generation, multistorage solutions on elliptic curves, and cryptographic competitions. Recent publications highlight advancements in isogeny-based security (2024), cryptographic Olympiad frameworks (2022), and integer factorization techniques using number-theoretic hints (2021). Earlier work (2019) addressed secure bit extraction from Koblitz curves. Sica previously collaborated with the NESSIE project at Université catholique de Louvain and worked at a crypto lab at the National University of Singapore. His work bridges theoretical number theory with practical cryptographic applications.

• Mathematics
• Number Theory
• Combinatorics
• +3 more

Chan Song Heng is an Associate Professor in the Division of Mathematical Sciences at the School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), Singapore. He has been affiliated with NTU since 2007. His academic journey includes a B.Sc. (Hons) in Mathematics from the National University of Singapore (2001) and a Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign (2005). His research focuses on advanced mathematical topics such as partition theory, q-series, mock theta functions, and number theory. Recent work includes studies on identities analogous to Jacobi, Fermat-Wilson theorems, and applications of Rogers-Fine identities. His publications explore combinatorial, analytic, and algebraic aspects of these fields, with notable contributions to modular forms, theta functions, and partition congruences. Dr. Chan’s articles often intersect with classical problems in mathematics, blending historical insights with modern analytical techniques. Notable themes include exploring identities through modular forms, analyzing partition statistics (ranks/cranks), and studying mock theta functions. Despite his prolific output, no specific scientific awards or student advisees are listed in the provided materials.

• Numerical Analysis
• Partial Differential Equations
• Finite Element Methods
• +4 more

Olaf Steinbach is a University Professor (Univ.-Prof.) at the Institute of Applied Mathematics at Graz University of Technology. His academic career spans over three decades with continuous research activity from 1992 to the present, including publications scheduled for 2026. He serves as a project manager for several research initiatives including the Special Research Area (SFB) F90 Computational Electric Machine Laboratory, which runs from 2022 to 2026. Professor Steinbach's research interests primarily focus on Numerical Analysis and Computational Mathematics . His work centers around developing and analyzing advanced numerical methods, particularly Finite Element Methods (FEM) and Boundary Element Methods (BEM), for solving partial differential equations (PDEs) and optimal control problems. His research spans both theoretical aspects (such as error analysis, stability, and convergence) and practical applications (including electric machines, electromagnetics, and biomechanics). He has made significant contributions to space-time finite element methods, which treat time as an additional dimension in the discretization process, leading to more robust and efficient solvers for time-dependent problems. Analysis of his recent publications (2021-2026) reveals a strong focus on optimal control problems governed by partial differential equations, with particular emphasis on elliptic, parabolic, and hyperbolic PDEs. His work demonstrates a consistent pattern of developing robust numerical methods with rigorous error analysis, often incorporating regularization techniques to handle challenging constraints. The applications span computational electromagnetics (particularly electric machines), fluid dynamics, and wave propagation problems. His research increasingly incorporates advanced computational techniques including parallel computing and isogeometric analysis. Professor Steinbach has supervised numerous doctoral students and has been actively involved in organizing academic events, including summer schools on Boundary Element Methods. His collaborative network extends across multiple disciplines and institutions, reflecting the interdisciplinary nature of his work in computational mathematics. His research has been supported through multiple significant projects including DK-W1244 Doctoral Program on Partial Differential Equations, the EU CASOPT project on optimization of industrial devices, and the ongoing Special Research Area on Computational Electric Machine Laboratory. These projects demonstrate his leadership in establishing research frameworks that bridge theoretical mathematics with practical engineering applications. Professor Steinbach maintains an active research group within the Institute of Applied Mathematics, collaborating closely with researchers in computational engineering, electrical engineering, and biomechanics. His work on the Computational Electric Machine Laboratory represents a particularly strong interdisciplinary effort combining mathematical theory with electrical engineering applications.

Christoph KehleView profile

Assistant Professor

• Analysis
• Partial Differential Equations
• General Relativity
• +3 more

Christoph Kehle is an Assistant Professor in the Department of Mathematics at the Massachusetts Institute of Technology (MIT) since 2024. He works at the intersection of General Relativity, Partial Differential Equations, and Mathematical Physics, focusing on black hole stability, cosmic censorship, and gravitational collapse phenomena. Education: PhD in Mathematics (2020) from the University of Cambridge under Mihalis Dafermos, MASt (2015) at Cambridge, and BS/MS (2016) from LMU Munich. Research: His work addresses fundamental questions about black hole interiors, extremal black hole formation, and nonlinear wave dynamics on curved spacetimes. He investigates connections between Diophantine approximation and spacetime stability, as well as turbulence in AdS black hole systems. Scientific Awards: Recipient of the Research Scholar at Trinity College (Cambridge), EPSRC PhD Scholarship, Senior Scholarship Exam Prize, and scholarships from the German Academic Foundation and Max Weber-Program. Publications: 15 most recent articles span nonlinear stability of extremal black holes, critical collapse phenomena, and geometric PDEs. Collaborators include Y. Angelopoulos, R. Unger, A. Figalli, and M. Van de Moortel.

Dond Asha KisanView profile

Assistant Professor

• Numerical Analysis
• Computational Mathematics
• Finite Element Methods
• +4 more

Dond Asha Kisan is an Assistant Professor at the School of Mathematics , Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM). His research focuses on numerical analysis and computational mathematics , particularly in finite element methods for partial differential equations. He can be contacted at ashadond@iisertvm.ac.in or via phone at +91 (0)471-2778247. PhD : Mathematics, Indian Institute of Technology Bombay M.Sc. : Mathematics, K.T.H.M. College, Nashik Kisan's research spans adaptive finite element methods , stabilized formulations for convection-diffusion problems , and optimal control governed by Stokes equations . His work includes convergence analysis, nonconforming discretizations, and hybrid numerical schemes. Recent publications (2023-2025) address stochastic modeling in liquid crystal physics, advanced WENO schemes, and adaptive algorithms for control problems. Scientific Awards : No explicit awards mentioned in the data, though he held prestigious postdoctoral fellowships including National Post-Doctoral Fellowship and NBHM Post-Doctoral Fellowship. Kisan has extensive teaching experience , including MATLAB workshops and undergraduate course assistantships. He has presented at major international conferences like ICIAM and Hyperbolic Problems, demonstrating global engagement in computational mathematics.

Xu JinchaoView profile

Professor

• Multigrid methods
• Machine learning
• Finite element methods
• +5 more

Xu Jinchao is a Professor of Applied Mathematics and Computational Sciences at King Abdullah University of Science and Technology (KAUST) and the Verne M. Willaman Professor of Mathematics at Penn State University. He has held distinguished roles, including Director of the Center for Computational Mathematics and Applications at Penn State since 1997 and is an Affiliated Faculty member of the College of Information Sciences and Technology at Penn State. His research focuses on numerical partial differential equations (PDEs), multigrid methods, machine learning, finite element methods, and domain decomposition methods. He is renowned for pioneering contributions such as the Bramble-Pasciak-Xu (BPX) preconditioner, Hiptmair-Xu (HX) preconditioner, Xu-Zikatanov (XZ) identity, and Morley-Wang-Xu (MWX) element. His work bridges computational mathematics and machine learning, including the development of MgNet, which unifies multigrid methods with convolutional neural networks. Xu has been recognized with numerous awards, including Fellowships from SIAM, AMS, AAAS, and the European Academy of Sciences. Notable accolades include the 2008 DOE Top 10 Breakthroughs for his HX preconditioner and the 1995 Feng Kang Prize for Scientific Computing. He has organized over 100 conferences and serves on editorial boards of top journals such as Mathematics of Computations and Numerische Mathematik . His leadership includes directing research centers and advancing computational science through collaborative efforts.

Jared WeinsteinView profile

Professor

• Number Theory
• Algebraic Geometry
• Arithmetic Geometry
• +3 more

Jared Weinstein is a Professor in the Department of Mathematics and Statistics at Boston University, serving as the Departmental Ombud. He specializes in Number Theory and Algebraic Geometry, with a focus on p-adic geometry, shtukas, and moduli spaces. His research explores connections between arithmetic geometry and homotopy theory, including contributions to the Langlands program and local Shimura varieties. Education: AB from Harvard University (undergraduate), PhD from University of California, Berkeley. Postdoctoral work at UCLA and the Institute for Advanced Study before joining BU in 2011. Research interests include arithmetic geometry, p-adic Hodge theory, and the geometry of moduli spaces. His work often intersects with topics like perfectoid spaces, diamonds, and chromatic homotopy theory. Recent articles highlight advancements in modularity of elliptic curves over function fields and the Kottwitz conjecture for local shtuka spaces. No scientific awards are explicitly listed, but his extensive publications reflect significant contributions to his field. Advising and grants details are not provided here. His work is closely tied to the v-topology and related geometric frameworks in algebraic geometry.

Markus BachmayrView profile

Professor

• Numerical Analysis
• Partial Differential Equations
• High-dimensional Problems
• +4 more

Prof. Dr. Markus Bachmayr is a full professor at the Institute for Geometry and Practical Mathematics, RWTH Aachen University, holding the chair for Applied Mathematics. His research focuses on nonlinear approximation, high-dimensional partial differential equations (PDEs), uncertainty quantification, and numerical methods in quantum chemistry. He leads the ERC Consolidator Grant project Computational Complexity of Highly Nonlinear Approximations (COCOA) and contributes to CRC 1481 Sparsity and Singular Structures, and RTG 2326 Energy, Entropy, and Dissipative Dynamics. His recent work emphasizes adaptive low-rank and sparse approximation techniques for parametric and stochastic PDEs, including applications in radiative transfer and poroviscoelastic flow modeling. He serves as Editor-in-Chief of Foundations of Computational Mathematics and Associate Editor for multiple journals. Scientific Awards: John Todd Award 2013 Borchers Plakette 2014 Erwin Wenzl Preis 2007 He has taught courses such as Numerische Analysis I/II, Numerische Mathematik für Elektrotechniker, and seminars on numerical methods and approximation theory.

Antonio De RosaView profile

Associate Professor

• Geometric Analysis
• Partial Differential Equations
• Geometric Measure Theory
• +3 more

Antonio De Rosa is an Associate Professor in the Department of Decision Sciences at Bocconi University, Italy. Previously, he held positions at the University of Maryland, College Park (2020–2024), and the Courant Institute of Mathematical Sciences, New York University (2017–2020). He earned his Ph.D. in Mathematics from the University of Zurich in 2017 under Camillo De Lellis and Guido De Philippis. Education: Ph.D. in Mathematics, University of Zurich (2017). His research spans Geometric Analysis , Partial Differential Equations , Calculus of Variations , Geometric Measure Theory , Optimal Transport , and Non-convex Optimization . Recent work focuses on anisotropic geometric variational problems, including existence, regularity, and uniqueness of anisotropic minimal surfaces and CMC (constant mean curvature) surfaces. He has also contributed to interdisciplinary applications in Explainable Risk Assessment and Data Analysis . The 15 most recent articles highlight advancements in anisotropic surfaces , min-max theory , optimal transport , and mathematical programming (e.g., K-means clustering, linear programming). Key trends include the intersection of geometric measure theory with nonlinear PDEs and applications in machine learning and transportation networks . Scientific Awards and Grants: 2023 Maryland Research Excellence Carlo Ciliberto Prize (2019) ERC Starting Grant ANGEVA (101076411, 2023–2028) Air Force Office of Scientific Research (AFOSR) grant (FA9550-23-1-0123) NSF CAREER Award (DMS-2143124) NSF DMS Awards (DMS-1906451, DMS-2112311) AMS Simons Travel Grant Antonio actively supervises research and teaches courses such as Optimization and Introduction to Partial Differential Equations . His work is supported by significant funding totaling approximately €3 million.

Svitlana MayborodaView profile

Professor

• Analysis and partial differential equations
• Wave localization
• Harmonic analysis
• +1 more

Svitlana Mayboroda is a Professor of Mathematics at ETH Zurich and the McKnight Presidential Professor at the University of Minnesota. Her research focuses on partial differential equations, harmonic analysis, and wave localization phenomena. University of Minnesota: School of Mathematics, 127 Vincent Hall, Minneapolis, MN ETH Zurich: Department of Mathematics, Ramistrasse 101, Zurich Research Interests: Analysis and partial differential equations Wave localization and Anderson localization Elliptic theory on non-smooth and lower-dimensional domains Harmonic measure and geometric measure theory Applications to quantum mechanics and semiconductor physics Recent Publications: Her 2023-2022 works investigate Anderson mobility edges, landscape functions in spectral theory, regularity problems for elliptic operators, and Green function estimates. Key themes include localization landscape theory, uniformly rectifiable domains, and spectral analysis of disordered systems. Grants & Collaborations: Simons Collaboration on Localization of Waves (Director, 2018–2025, $14M) NSF RAISE–TAQS grant ($1M) Academic Leadership: She has organized numerous conferences and workshops, including annual meetings of the Simons Collaboration on Wave Localization (2020–2024) and programs at MSRI and PCMI. Her mentorship includes postdocs and PhD students working on elliptic theory, spectral problems, and applied mathematical physics.

John LottView profile

Professor

• Differential geometry
• Geometric analysis
• Ricci curvature
• +6 more

John Lott is a Professor in the Department of Mathematics at the University of California, Berkeley, specializing in Differential Geometry , Geometric Analysis , and Optimal Transport since his appointment in 2008. His research explores the interplay between Ricci curvature , metric-measure spaces , and geometric flows , with notable contributions to Ricci flow and noncommutative geometry . He has supervised multiple PhD students including Thunwa Theerakarn and Patrick Wilson , and maintains an active publication record with over 40 research papers. Selected Research Areas : Differential Geometry, Geometric Analysis, Optimal Transport, Mathematical Physics, Noncommutative Geometry Recent Publications (2020-2025) focus on Kähler manifolds , collapsing geometry , and quasilocal mass in general relativity. His work on Ricci curvature via optimal transport with Cédric Villani has become foundational in the field. Academic Affiliation : Position: Professor Institution: University of California, Berkeley Department: Mathematics

Dhruv RanganathanView profile

Professor

• Algebraic Geometry
• Enumerative Geometry
• Gromov-Witten Theory
• +4 more

Professor Dhruv Ranganathan is affiliated with the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, working within the Algebraic Geometry research group. His research spans foundational and applied aspects of algebraic geometry, focusing on enumerative geometry, Gromov-Witten theory, moduli spaces, tropical geometry, logarithmic structures, and classical geometry of curves. Research Focus Enumerative geometry and Gromov-Witten theory, particularly in toric varieties and tropical settings. Moduli spaces of curves and stable maps, with expansions and logarithmic structures. Applications of tropical geometry to classical problems in algebraic geometry. Brill-Noether theory and its combinatorial analogues for graphs and finite structures. Recent Publications The articles reflect a strong emphasis on logarithmic and tropical geometry, with connections to moduli spaces, enumerative invariants, and combinatorial algebraic structures. Topics include Donaldson–Thomas theory, double ramification cycles, chip firing on graphs, and motivic zeta functions. Contact Email: dr508@dpmms.cam.ac.uk Room: E1.01, Telephone: 01223 337990 Personal Homepage

Nathan KaplanView profile

Professor

• Number Theory
• Algebraic Geometry
• Combinatorics
• +6 more

Nathan Kaplan is a Professor in the Department of Mathematics at the University of California, Irvine, where he conducts research in number theory, algebraic geometry, and combinatorics. His work spans rational points on varieties over finite fields, arithmetic statistics, coding theory, and the study of numerical semigroups. He is actively involved in the mathematical community, organizing seminars and conferences including the UC Irvine Number Theory Seminar and the Southern California Number Theory Day. Dr. Kaplan received his PhD from Harvard University in 2013 under the direction of Noam Elkies. Following his doctorate, he was a postdoctoral researcher at Yale University from 2013-2015 before joining the faculty at UC Irvine. His research interests focus on the intersection of number theory and algebraic geometry, with particular attention to problems involving rational points on varieties over finite fields, arithmetic statistics, and coding theory. He has made significant contributions to the study of numerical semigroups, cokernels of random p-adic and integer matrices, and quadratic forms and lattices. His work often bridges theoretical mathematics with applications in coding theory and cryptography. Analysis of his recent publications shows a strong trend toward combinatorial aspects of number theory, particularly in the study of numerical semigroups and their properties. He frequently collaborates with researchers across institutions, with recent work spanning algebraic geometry, combinatorics, and coding theory. His publications demonstrate expertise in both theoretical developments and computational aspects of number theory. Dr. Kaplan is deeply committed to undergraduate research and mentoring. He has experience as a mentor for undergraduate research projects through programs including SUMRY (a research program for Yale undergraduates), the University of Minnesota-Duluth REU program, and the Trinity University REU program. He actively encourages undergraduates to apply for summer research opportunities and has organized numerous outreach activities. He is an organizer of the UC Irvine Number Theory Seminar and the Southern California Number Theory Day conference series. In 2018, he co-organized the Conference on Open Questions in Cryptography and Number Theory in honor of Alice Silverberg's 60th Birthday. Dr. Kaplan has given numerous talks at mathematical venues including the Museum of Mathematics' Math Encounters series, where he presented "Error-Correcting Codes: The Mathematics of Communication" in July 2022. He has also spoken at the Yale Undergraduate Math Society, the UCI Math Circle, and various other outreach events.

Lakshmi N SankarView profile

Professor

• Aerodynamics
• Fluid Mechanics
• Computational Fluid Dynamics
• +5 more

Lakshmi N Sankar serves as Regents Professor and Sikorsky Professor in the Guggenheim School of Aerospace Engineering at Georgia Institute of Technology, where he directs the Computational Fluid Dynamics Laboratory and teaches aerodynamics, helicopter theory, and wind energy courses. His research program spans unsteady viscous flow modeling for aircraft, helicopters, and wind turbines since joining the faculty in 1982 after industry experience at Lockheed Martin. Education: Ph.D., Aerospace Engineering, Georgia Institute of Technology, 1977 MSAE, Aerospace Engineering, Georgia Institute of Technology, 1975 B. Tech., Aeronautical Engineering, Indian Institute of Technology, Madras, India, 1973 Research Focus: Professor Sankar's work centers on Computational Fluid Dynamics for rotorcraft aerodynamics and wind energy systems , with significant contributions to icing phenomena and unsteady flow modeling . His recent publications reveal intensifying focus on adverse weather effects (rain/icing), eVTOL conversion challenges, and high-fidelity hybrid modeling techniques for rotorcraft performance prediction. Publication Trends: Analysis of his 2022-2025 publications shows dominant themes in rotorcraft icing (35%), weather impact studies (25%), and advanced CFD methodologies (20%), with growing interest in drone applications and mathematical aspects of fluid dynamics. His work consistently bridges theoretical mathematics with practical aerospace engineering challenges. Scientific Recognition: AIAA Fellow and AHS Technical Fellow NASA Group Achievement Award (2007) and Space Act Software Release Award (2003) Multiple Sigma Gamma Tau Teaching Awards (2005-2015) Dean George C. Griffin Faculty of the Year (2014-2015) Sikorsky Professorship (2018-Present) Mentorship and Collaboration: As recipient of Georgia Tech's Graduate Research Assistant Development Award, he has cultivated extensive student mentorship. His research integrates with the Vertical Lift Research Center of Excellence and Center for 21st Century Universities, securing major industry and NASA funding for rotorcraft innovation. Current projects include physics-based modeling of ice accretion and eVTOL retrofit feasibility studies. Research Infrastructure: The Computational Fluid Dynamics Laboratory serves as his primary research hub, complemented by collaborations through the Vertical Lift Research Center of Excellence where his team develops next-generation modeling tools for military and civilian rotorcraft applications under federal funding programs.