جستجوی استاد راهنمای دانشگاهی

Kenneth McLaughlinمشاهده پروفایل

استاد

• Integrable Systems
• Mathematical Physics
• Nonlinear Dynamics
• +۳ مورد دیگر

Kenneth McLaughlin is the Evelyn and John G. Phillips Distinguished Chair in Mathematics at Tulane University's School of Science & Engineering. He holds a Ph.D. and B.A. in Mathematics from New York University (1994 and 1989). Prior to Tulane, he served as faculty at the University of North Carolina, Chapel Hill, the University of Arizona, Universidade Federal de Brasília, and Colorado State University, where he also held leadership roles as Department Head and Chair. His research focuses on integrability, applying techniques across mathematics to study complex systems and phenomena. He has held visiting positions at institutions worldwide, including France, Italy, Brazil, Belgium, and the UK. McLaughlin’s research spans integrable systems, nonlinear dynamics, and asymptotic analysis. His work often involves the Riemann-Hilbert problem approach, orthogonal polynomials, and random matrix theory. Notable contributions include studies on soliton gases, the KdV equation, and universality in quantum operator dynamics. His recent articles explore topics such as asymptotic behavior of polynomials, soliton gas condensation, and hydrodynamic limits in integrable systems. McLaughlin’s academic career is marked by interdisciplinary collaboration and international research engagement.

David Jerisonمشاهده پروفایل

استاد

• Fourier analysis
• partial differential equations
• free boundary problems
• +۲ مورد دیگر

David Jerison is a Professor of Mathematics at the Massachusetts Institute of Technology (MIT), where he conducts research in Fourier analysis and partial differential equations. His work focuses primarily on free boundary problems and, more recently, on internal Diffusion Limited Aggregation (internal DLA), a stochastic growth model. He maintains an active research program with numerous publications in leading mathematical journals. Professor Jerison's research spans several interconnected areas of mathematical analysis. His primary interests include Fourier analysis and partial differential equations, with particular emphasis on free boundary problems. In recent years, he has expanded his research to include internal Diffusion Limited Aggregation, a stochastic growth model that has connections to probability theory and mathematical physics. His work often bridges geometric analysis, spectral theory, and probabilistic methods, demonstrating the deep connections between different branches of mathematics. Analysis of Professor Jerison's recent publications reveals a consistent focus on geometric aspects of partial differential equations, particularly free boundary problems. His research shows progression from classical PDE theory toward more stochastic and probabilistic approaches, as evidenced by his work on internal DLA. The publications demonstrate interdisciplinary connections between mathematical analysis, probability theory, and mathematical physics, with applications ranging from geometric measure theory to quantum mechanics. Professor Jerison is actively involved in teaching and mentoring at MIT. He has taught courses including Differential Equations (18.03), Fourier Analysis and Applications (18.103), and Differential Analysis (18.155). He also directs the Summer Program for Undergraduate Research (SPUR), which is exclusively for MIT undergraduates, and organizes the mathematics section of the Research Science Institute (RSI) for high school students. His teaching materials are available through MIT's Open Courseware platform, indicating his commitment to educational outreach and accessibility.

Lenya Ryzhikمشاهده پروفایل

استاد

• Partial Differential Equations
• Analysis
• Applied Mathematics
• +۵ مورد دیگر

Lenya Ryzhik is a Professor in the Department of Mathematics at Stanford University, specializing in analysis and partial differential equations with applications in various physical contexts. His research spans stochastic processes, wave propagation, and front dynamics in random media, with significant contributions to understanding reaction-diffusion systems and their applications in mathematical biology and physics. Professor Ryzhik's research interests focus on the mathematical analysis of partial differential equations arising in physical systems. His work particularly emphasizes stochastic PDEs, wave propagation in random media, front propagation in reaction-diffusion systems, and homogenization theory. He investigates how randomness and complex structures affect wave propagation, front speeds, and transport phenomena, with applications ranging from combustion theory to population dynamics and quantum mechanics. The publication record demonstrates a consistent focus on understanding propagation phenomena in complex environments. Ryzhik's research shows a progression from classical PDE analysis toward increasingly sophisticated stochastic frameworks, particularly examining high-dimensional systems and random media. His recent work has focused on KPZ fluctuations, random heat equations, and non-local reaction-diffusion models, revealing deep connections between probability theory and partial differential equations. Alfred P. Sloan Research Fellowship (2002-2004) AFOSR NSSEFF Fellowship (2010-2015) Ryzhik has advised graduate students including Alexandra Stavrianidi, and has secured substantial research funding throughout his career. His grant history includes multiple NSF awards (DMS-9971742, DMS-0203537, DMS-0604687, DMS-0908507, DMS-1311903), ONR funding (N00014-02-1-0089, N00014-04-1-0224), and FRG support for collaborative research on nonlinear evolution problems. He co-organized a Summer School and Workshop on 'Recent Advances in PDEs and Fluids' at Stanford in 2013. Ryzhik maintains an active research group collaborating with leading mathematicians worldwide, particularly with researchers at institutions like NYU, Chicago, and various European universities. His work frequently involves interdisciplinary collaborations bridging mathematics with physics and biology.

David Damanikمشاهده پروفایل

استاد

• Spectral Theory
• Dynamical Systems
• Aperiodic Order
• +۳ مورد دیگر

David Damanik is the Robert L. Moody, Sr. Professor of Mathematics at Rice University, where he has established himself as a leading researcher in spectral theory, dynamical systems, and aperiodic order. His work bridges pure mathematics with mathematical physics, focusing on the spectral properties of operators arising in quantum mechanics and quasicrystal theory. Dr. Damanik received his academic training at Johann Wolfgang Goethe-Universität in Frankfurt, Germany, earning a Dipl.-Math. in 1995, Dipl.-Inform. in 1996, and Dr. phil. nat. in 1998. His educational background reflects a strong foundation in both mathematics and computer science, which informs his interdisciplinary research approach. His research interests center around spectral theory of Schrödinger operators, particularly those with ergodic, quasi-periodic, and aperiodic potentials. He has made significant contributions to understanding the spectral properties of operators associated with quasicrystals, substitution sequences, and other aperiodic structures. His work often connects spectral properties with dynamical systems concepts, particularly through the study of rotation numbers, Lyapunov exponents, and gap labeling theorems. Damanik's research has profound implications for understanding quantum transport in aperiodic media and the mathematical foundations of condensed matter physics. Analysis of his recent publications (2022-2024) reveals a continued focus on ergodic Schrödinger operators, with two comprehensive monographs providing a systematic treatment of the field. His work spans both theoretical foundations and specific applications, addressing problems in one-dimensional systems, quasi-periodic potentials, and aperiodic tilings. The research demonstrates strong connections between spectral theory, dynamical systems, and mathematical physics, with particular emphasis on the interplay between spectral properties and the underlying dynamics of the potential. Annales Henri Poincaré Prize (2014) for the paper "Continuum Schrödinger operators associated with aperiodic subshifts" Professor Damanik has mentored numerous PhD students and maintains an extensive network of collaborators across the globe, as evidenced by his long list of coauthors. His research has been supported by various grants that enable him to organize workshops and conferences, fostering collaboration in his field. He has been instrumental in organizing major conferences such as the Spectral Theory and Mathematical Physics conference honoring Barry Simon's 80th birthday (scheduled for 2026) and multiple workshops on aperiodic order at prestigious institutions like Banff International Research Station and Mathematisches Forschungsinstitut Oberwolfach. Through his teaching of specialized courses like "Mathematics of Aperiodic Order" and "Ergodic Theory and Topological Dynamics," Damanik has cultivated the next generation of researchers in his field. His leadership in organizing conferences and workshops has established him as a central figure in the international community studying spectral theory and aperiodic structures.

Scott Armstrongمشاهده پروفایل

استاد

• Partial Differential Equations
• Calculus of Variations
• Probability Theory
• +۳ مورد دیگر

Scott Armstrong is a Professor of Mathematics at the Courant Institute of Mathematical Sciences, New York University. His research focuses on partial differential equations, calculus of variations, and probability theory, with a specialization in stochastic homogenization of PDEs in random media and related statistical mechanical systems. He holds a Ph.D. from UC Berkeley (2009) and a B.S. from Texas A&M University (2002). Education: Ph.D. in Mathematics, University of California, Berkeley, USA (2009) B.S. in Mathematics, Texas A&M University, USA (2002) Research Interests: Scott's work addresses fundamental questions in homogenization theory, including quantitative estimates for elliptic and parabolic equations in random media, renormalization group methods, and applications to statistical mechanics. His contributions bridge analysis, probability, and mathematical physics, with a focus on rigorous mathematical frameworks for understanding macroscopic behavior from microscopic models. Publications: His recent work includes studies on anomalous diffusion, renormalization group techniques, and quantitative homogenization in high-contrast media. Over 50 peer-reviewed articles highlight his expertise in stochastic PDEs, elliptic regularity, and variational methods. Awards: No specific awards listed in the provided text. Advising & Grants: No student advisees or grant details explicitly mentioned in the text. Labs/Teams: No dedicated labs or collaborative teams explicitly noted, though his research likely involves interdisciplinary collaborations within the Courant Institute.

Rupert Frankمشاهده پروفایل

استاد

• Analysis
• Mathematical Physics
• Spectral Theory
• +۸ مورد دیگر

Rupert Frank is a Professor of Mathematics at the University of Munich (LMU Munich) . He has held academic positions at Caltech (2013–2021) and Princeton University (2009–2013). His research spans Mathematical Physics , Spectral Theory , and Functional Inequalities , with a focus on quantum many-body systems, stability of matter, and nonlocal operators. Research Themes : Analysis of eigenvalues for Schrödinger and Pauli operators with complex potentials Semi-classical spectral asymptotics and effective theories for quantum systems Matrix inequalities and quantum information theory Calculus of variations in models like the liquid drop problem Geometric inequalities and their applications to quantum mechanics Magnetic field effects on spectral properties Recent Publications : 2025: Sharp stability for Sobolev/log-Sobolev inequalities with dimensional dependence 2025: Endpoint Schatten class properties of commutators 2024: Degenerate stability of Caffarelli-Kohn-Nirenberg inequality 2024: Hardy inequalities for large fermionic systems 2023: Review on Scott conjecture for Coulomb systems Scientific Awards : Young Scientist Prize in Mathematical Physics (2009) Grants and Collaborations : Principal Investigator in CRC TRR 352 (2023–) PI in Munich Center for Quantum Science and Technology (2019–) Multiple NSF grants (2009–2020) DFG and DAAD grants Editorial and Conference Leadership : Editorial boards: Communications in Mathematical Physics , Journal in Mathematical Physics , Journal of Spectral Theory , SIAM Journal on Mathematical Analysis , Springer Lecture Notes Organized conferences/workshops on quantum many-body systems, spectral methods, and functional inequalities (2018–2025)

Werner Ballmannمشاهده پروفایل

استاد

• Differential Geometry
• Geometric Analysis
• Nonpositive Curvature
• +۳ مورد دیگر

Werner Ballmann is a renowned mathematician specializing in differential geometry and geometric analysis. He served as Full Professor at the University of Bonn (1989–2016) and the University of Zürich (1987–1989). Since 2007, he has been a Scientific Member and Director of the Max Planck Institute for Mathematics (2007–2019). His research focuses on nonpositive curvature, spectral theory, and geometric structures on manifolds. Ballmann holds a Diplom (1976) and Promotion (1979) from the University of Bonn, with a Habilitation in 1984. His work includes groundbreaking studies on the geometry of manifolds, hyperbolic spaces, and orbifolds. Recent articles address spectral instability, eigenvalue analysis, and stochastic processes on geometric structures. Notable contributions include investigations into Martin boundaries, diffusion discretizations, and the interplay between geometry and spectral properties. Ballmann has authored influential textbooks such as Lectures on Kähler Manifolds (2006) and Introduction to Geometry and Topology (2018). His research bridges geometric analysis, topology, and probability, with applications in manifold theory and group actions.

Ovidiu Costinمشاهده پروفایل

استاد

• Mathematical Physics
• Differential Equations
• Asymptotics
• +۷ مورد دیگر

Ovidiu Costin is a Professor of Mathematics at The Ohio State University's Department of Mathematics, College of Arts and Sciences. His research focuses on mathematical physics, differential equations, asymptotics, and resurgence theory. He holds a PhD from Rutgers University (1995) and has authored numerous influential papers on topics such as Borel summability, Painlevé equations, and quantum dynamics. Education: PhD in Mathematics from Rutgers University, awarded in 1995. Research Interests: Resurgence theory, asymptotic analysis, integrable systems, spectral theory, and complex dynamics. His work bridges pure and applied mathematics, with applications in quantum mechanics and nonlinear dynamics. His recent articles explore non-perturbative solutions of Schrödinger equations, Borel summability in PDEs, and the analysis of singularities in nonlinear systems. Notable contributions include the proof of the Dubrovin conjecture and foundational work on transseries and surreal numbers. Scientific Awards: Recipient of the Guggenheim Fellowship. His research has been supported by NSF grants, including DMS-0103807, DMS-1515755, and others. Teaching: He teaches advanced courses in real and complex analysis, functional analysis, and applied mathematics. Office: Math Tower 404; email: costin.9@osu.edu.

Shuangping Liمشاهده پروفایل

استادیار

• Probability Theory
• High-Dimensional Statistics
• Theoretical Machine Learning
• +۵ مورد دیگر

Shuangping Li is an Assistant Professor in the Department of Statistics and Data Science at Yale University. She was previously a Stein Fellow in the Department of Statistics at Stanford University (2022–2025). Her research lies at the intersection of probability theory, high-dimensional statistics, theoretical machine learning, and the theory of algorithms. Ph.D. in Applied and Computational Mathematics, Princeton University (2022) B.Sc. in Mathematics, University of Hong Kong Her research interests include probability theory , high-dimensional statistics , theoretical machine learning , and theory of algorithms . She investigates foundational aspects of random constraint satisfaction problems, neural networks, spectral methods, and phase transitions in high-dimensional models. Her work often draws from statistical physics and combinatorics to explain algorithmic behavior. The recent articles highlight a strong focus on binary perceptrons , clustering in network models , and algorithmic phase transitions . Keywords across publications include probability, theoretical computer science, machine learning, and statistical inference. Subfields reveal deep engagement with spin glass theory, discrepancy minimization, spectral embedding, and information-computation gaps. Scientific awards include: Stein Fellow, Department of Statistics, Stanford University (2022–2025) She has advised and taught at both Stanford and Yale, including courses such as Advanced Probability , Theory of Probability , and Stochastic Processes . She has organized seminars at Stanford and has delivered invited talks at institutions including Cornell, Duke, UC Berkeley, and Princeton. Her collaborative research involves prominent scholars such as Allan Sly, Emmanuel Abbe, and Tselil Schramm. There is no mention of external grants, but her postdoctoral fellowship suggests research funding support. She is involved in academic service through organizing the Stanford Statistics and Probability Seminars. She maintains an active research presence with publications in top venues like STOC, FOCS, COLT, ICLR, and journals such as Annals of Probability and Annals of Statistics .

Hugo Georges Victor Lavenantمشاهده پروفایل

استادیار

• Optimal Transport
• Calculus of Variations
• Convex Analysis
• +۳ مورد دیگر

Hugo Georges Victor Lavenant serves as Assistant Professor in the Department of Decision Sciences at Bocconi University, Milan, where he has held a faculty position since 2020. Previously, he completed a postdoctoral fellowship at the University of British Columbia (2019-2020) under the Pacific Institute of Mathematical Sciences and earned his PhD in Mathematics from Université Paris-Sud (2016-2019) under Filippo Santambrogio's supervision. His academic foundation includes: PhD in Mathematics, Université Paris-Sud (2016-2019) Studies at École Normale Supérieure (2012-2016) covering mathematics, physics, history, and philosophy of science Classes préparatoires in mathematics and physics (2010-2012) Lavenant's research centers on optimal transport theory and its applications across mathematical disciplines. He investigates geometric structures in Wasserstein spaces, develops numerical methods for dynamical optimal transport, and bridges theoretical advances with Bayesian statistics. His work demonstrates particular innovation in trajectory inference for biological data and dependence measures for random measures, connecting pure mathematics with computational statistics. Recent publications reveal accelerating interdisciplinary impact, with 2024-2025 works extending optimal transport to machine learning (kernel methods, variational inference) and data science (opinion dynamics, single-cell analysis). This trajectory shows increasing methodological sophistication in handling measure-valued mappings and non-smooth geometries while maintaining computational tractability. Award recognition includes: Pacific Institute of Mathematical Sciences Postdoctoral Fellowship Lavenant actively mentors early-career researchers through formal advising relationships and collaborative projects. He currently supervises two PhD candidates (George Kanchaveli and Francesco Mascari, co-advised with Marta Catalano) and has guided Master's students including Mathis Hardion and Niccolò Bargellini. His teaching portfolio spans advanced analysis, optimization, and real analysis courses at Bocconi, reflecting his commitment to mathematical rigor in education. He operates within Bocconi's Decision Sciences ecosystem while maintaining international collaborations with researchers at UBC, Université Paris-Sud, and statistical groups worldwide. Current projects focus on entropy-based transport methods and geometric approaches to nonparametric statistics, positioning his work at the intersection of theoretical mathematics and data-driven applications.

• Mathematical Physics
• Partial Differential Equations
• Probability
• +۳ مورد دیگر

Felipe Hernández is an Assistant Professor in the Department of Mathematics at Pennsylvania State University. He is affiliated with the Department of Mathematics, located in McAllister Building, and can be contacted at felipeh@psu.edu. His research interests span Mathematical Physics, Partial Differential Equations, and Probability, with a focus on quantum systems, stochastic processes, and theoretical analysis of complex systems. His work explores topics such as quantum diffusion in disordered systems, decoherence dynamics, and the interplay between classical and quantum mechanics. He also investigates computational methods like neural networks to enhance accuracy in quantum chemistry calculations and explores foundational questions in quantum computing, such as BosonSampling complexity. Recent contributions include studies on Hodge systems, divergence-free vector fields, and endpoint estimates in functional analysis. While no specific awards or grants are listed, his research demonstrates a commitment to advancing mathematical physics and computational methods through rigorous theoretical analysis and interdisciplinary approaches.

Patricia Alonso Ruizمشاهده پروفایل

دانشیار

• Analysis
• Probability
• Fractal Geometry
• +۳ مورد دیگر

Patricia Alonso Ruiz is an Associate Professor in the Department of Mathematics at Texas A&M University (on leave AY24/25). She specializes in analyzing random phenomena in fractal-like environments, focusing on connections between analysis, probability, and geometry. Her research involves Dirichlet forms, heat kernels, and stochastic processes on fractals such as the Sierpinski gasket and diamond fractals. Her academic journey includes leadership in the TAMU Fractals Research Team, supported by an NSF grant. She has organized conferences like the BIRS Workshop on New Trends in Stochastic Analysis and the Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals. Her outreach efforts include the Kenya Workshop and educational programs like the Summer Educational Enrichment in Math. Key research areas include spectral theory of fractals, BV functions on metric measure spaces, and functional inequalities in fractal settings. Collaborations with researchers like Fabrice Baudoin and Alexander Teplyaev have yielded impactful work on heat kernel analysis and Besov spaces. She mentors undergraduate teams exploring spectral features of fractals, fostering the next generation of mathematicians. Publications span topics from nonlocal energies to Orlicz-Sobolev embeddings, reflecting her interdisciplinary approach bridging pure and applied mathematics. Her work highlights the interplay between fractal geometry and stochastic analysis, advancing understanding of complex systems in porous and non-smooth environments.

Xue-Mei Liمشاهده پروفایل

استاد

• Stochastic Analysis
• Geometric Stochastic Analysis
• Malliavin Calculus
• +۵ مورد دیگر

Xue-Mei Li is a Professor of Mathematics at Imperial College London and École Polytechnique Fédérale de Lausanne (EPFL). She holds chairs in Probability and Stochastic Analysis at both institutions. Her research focuses on stochastic analysis, geometric stochastic processes, and multi-scale systems, with contributions to areas like Malliavin calculus, fractional dynamics, and coarse curvature. Li has held positions at the University of Warwick, University of Connecticut, and others, supported by fellowships from the Alexander von Humboldt Foundation, Royal Society, and MSRI. Her work addresses fundamental questions in stochastic differential equations, geometric analysis, and their applications to complex systems. Education and Career: PhD in Mathematics, University of Warwick EPSRC Research Associate Faculty positions at the University of Connecticut (tenured Associate Professor) Research Interests: Her research spans stochastic differential equations (SDEs), stochastic partial differential equations (SPDEs), geometric stochastic analysis, and fractional dynamics. Notable contributions include the BEL formula, strict local martingales, and solutions to longstanding problems in strong completeness on non-compact manifolds. She explores interactions between stochastic processes and geometric structures, including coarse Ricci curvature and homogenization theory. Awards and Grants: Supported by NSF, EPSRC/UKRI, and Swiss NSF grants Awarded fellowships from Alexander von Humboldt Foundation, Royal Society, and MSRI Advising and Teams: PhD students: Johann Gehringer, Rhys Steel, Julian Sieber, and others Leading working groups on stochastic analysis and geometric dynamics

• Stochastic Analysis
• Random Walks
• Percolation Theory
• +۱ مورد دیگر

Sebastian Andres is Professor of Stochastics at TU Braunschweig's Institute of Mathematical Stochastics. His research focuses on random processes in disordered media, including homogenization of random walks, percolation theory, and heat kernel analysis. He holds a habilitation from University of Bonn and previously held positions at University of Cambridge and University of Manchester. Research Themes: Quantitative homogenization, invariance principles for degenerate random walks, and applications to mathematical physics. Teaching: Current courses include Probability Theory and Discrete Financial Mathematics; authored lecture notes on Martingale Theory for Finance.

• Mathematical Physics
• Analysis
• Probability Theory
• +۴ مورد دیگر

Prof. Dr. Peter Müller is a Professor at the Mathematical Institute of Ludwig Maximilian University of Munich (LMU), where he also serves as Dean of the Faculty of Mathematics, Informatics and Statistics. His research group focuses on Analysis, Mathematical Physics, and Numerics. Office: Room 439, Block B, Theresienstr. 39, 80333 Munich. Education: Habilitation in Mathematics, University of Göttingen (2006) Habilitation in Physics, University of Göttingen (2002) Ph.D. in Physics, University of Erlangen-Nürnberg (1996) Diploma in Physics, University of Erlangen-Nürnberg (1991) Research Interests: Müller's work spans mathematical physics, analysis, and probability theory, with emphasis on: Random Schrödinger operators and spectral theory Delocalization phenomena in disordered systems Quasiperiodic structures and ergodic properties Entanglement entropy in quantum systems His research bridges rigorous mathematical analysis with applications in quantum mechanics and statistical physics. Publication Trends: Recent articles (2013–2025) predominantly explore spectral theory in disordered quantum systems. Key themes include localization/delocalization transitions, asymptotic analysis of entanglement entropy, and spectral properties of random operators. Methodologically, his work combines functional analysis, stochastic processes, and operator theory to address fundamental questions in mathematical physics. Student Advising: Extensive mentorship of graduate students: 8 PhD students (e.g., Jakob Stern, Ruth Schulte) 17 Master's students (e.g., Leonard Wetzel, Julian Widl) Research Team: Leads the working group "Analysis, Mathematical Physics and Numerical Analysis" with postdoctoral researchers (e.g., Constanza Rojas-Molina) and PhD candidates. Regularly organizes international conferences on mathematical physics and disordered systems.