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Wendelin Werner is a renowned mathematician and currently the Rouse Ball Professor of Mathematics at the University of Cambridge (since 2023). Previously, he held professorships at ETH Zürich (2013–2023) and the University of Paris-Sud in Orsay (1997–2013). His research focuses on probability theory, mathematical physics, and complex analysis, particularly Schramm-Loewner evolution and conformal invariance. He has received prestigious awards, including the Fields Medal (2006), SIAM George Pólya Prize (2006), and Fermat Prize (2001). His work bridges stochastic processes and geometric structures, with implications for statistical mechanics and critical phenomena. Werner studied at the École Normale Supérieure (1987–1991) and earned his PhD from Université Paris VI under J. F. Le Gall (1993). Early career positions included postdoctoral research at Cambridge (1993–1995) and roles at CNRS (1991–1993, 1995–1997). His academic contributions span stochastic geometry, critical systems, and random curves, with seminal papers on loop measures, percolation, and SLE. He has delivered major lectures globally, including at the International Congress of Mathematicians (IMC 2006) and the College de France's Cours Peccot. Werner’s honors include membership in the French Academy of Sciences (2008), the Berlin-Brandenburg Academy (BBAW), and the German National Academy Leopoldina. He is also an honorary fellow of Gonville and Caius College, Cambridge (2009). His research has advanced understanding of universal scaling limits in two-dimensional models, earning recognition as a leader in probability and mathematical physics.

• Schramm-Loewner Evolution
• Probability Theory
• Mathematical Physics
• +3 more

Stanislav Smirnov is a Professor of Mathematics at the University of Geneva, where he has been a faculty member since 2003. He also holds a part-time position at the Chebyshev Laboratory of St. Petersburg State University. As Director of the National Centre of Competence in Research SwissMAP since 2014, he leads a major research initiative funded by the Swiss National Science Foundation. His education includes a mathematics degree from St. Petersburg State University (1992) and a PhD from the California Institute of Technology (1996). Prior to joining Geneva, he held positions at Yale University, the Institute for Advanced Study in Princeton, the Max Planck Institute in Bonn, and the Royal Institute of Technology in Stockholm. Professor Smirnov's research focuses on the mathematical foundations of statistical physics, with particular emphasis on conformal invariance in two-dimensional lattice models. His work has revolutionized our understanding of critical phenomena through rigorous mathematical approaches, establishing deep connections between probability theory, complex analysis, and statistical mechanics. He develops novel discrete complex analysis techniques to prove continuum limits of lattice models at criticality. His publication record shows consistent advancement in understanding random planar geometry, percolation theory, and the Ising model, with increasing attention to Liouville quantum gravity in recent years. His work bridges deep mathematical analysis with physical insights, often providing rigorous proofs for phenomena previously understood only through physical intuition. Fields Medal (2010) for the proof of conformal invariance of percolation and the planar Ising model in statistical physics As an advisor, Professor Smirnov has mentored doctoral students including Ekin Arikök and Nikolai Bobenko. He leads the ANALYSE, PHYSIQUE MATHÉMATIQUE ET PROBABILITÉS research group at the University of Geneva. His research is supported by major grants including the NCCR SwissMAP, European Research Council's AG COMPASP, and Swiss National Science Foundation grants 200020_143434 and 200020_141329. Professor Smirnov has organized numerous influential conferences, including the "Conformal maps from probability to physics" workshop at Monte Verità (2010) and multiple "Random Planar Geometry" meetings in Les Diablerets, fostering collaboration between mathematicians and physicists working on critical phenomena and random geometry.

• Mathematical Physics
• Statistical Physics
• Probability Theory
• +4 more

Stanislav Smirnov is a Professor at the University of Geneva's Department of Mathematics since 2003 and Head of the Chebyshev Laboratory at St. Petersburg State University since 2010. He holds a Ph.D. from the California Institute of Technology (1996) and a B.Sc./M.Sc. from St. Petersburg State University (1992). His research focuses on mathematical physics, probability, complex analysis, and dynamical systems, with groundbreaking contributions to the understanding of critical phenomena in statistical physics. Key achievements include receiving the Fields Medal (2010), the highest honor in mathematics, for his work on percolation and the Ising model. He has organized major international conferences, such as the 'St. Petersburg School in Probability & Statistical Physics' (2012) and the '2D Statistical Physics Workshop' (2013). His academic career includes positions at Yale University, the Max-Planck Institute, and KTH Royal Institute of Technology. Education: Ph.D., Mathematics, California Institute of Technology (1996) B.Sc./M.Sc., Mathematics (with honors), St. Petersburg State University (1992) Awards: Fields Medal (2010) European Research Council Advanced Grants (2008, 2013) Rollo Davidson Prize (2002) Salem Prize (2001) Smirnov’s research bridges probability theory and complex analysis, with notable results on conformal invariance in two-dimensional models. His work has advanced understanding of critical exponents, percolation thresholds, and the universality of phase transitions. He advises doctoral students and collaborates internationally on projects funded by Swiss and European grants. He co-organized over 20 conferences worldwide, including plenary talks at the International Congress of Mathematicians (2006, 2010) and the World Congress in Probability and Statistics (2012). His lab fosters interdisciplinary research, linking mathematics to physics and computer science.

• Mathematical Physics
• Probability
• Complex Analysis
• +3 more

Ewain Gwynne is a Professor of Mathematics at the University of Chicago, affiliated with the Committee on Computational and Applied Mathematics (CCAM) and the Statistics Department. He previously held postdoctoral positions at the University of Cambridge and earned his Ph.D. from MIT in 2018 under Scott Sheffield. His research focuses on probability theory, particularly random geometric structures in statistical mechanics, including Schramm-Loewner evolution (SLE), Liouville quantum gravity (LQG), and random planar maps. Education: Ph.D. in Mathematics, MIT (2018); M.Sc., MIT (2015); B.Sc., Northwestern University (2013). Research Interests: Random geometric objects in statistical mechanics Liouville quantum gravity and its metric properties Random planar maps and their scaling limits SLE and its relationship with LQG Random walks on random planar maps Percolation and permutons His recent articles explore topics such as supercritical LQG, Gaussian curvature on random maps, and harmonic balls in LQG. He has advised multiple Ph.D. students and serves as an associate editor for Probability and Mathematical Physics . His work bridges probability theory, geometry, and mathematical physics, with applications to understanding critical phenomena in random systems.

• Probability Theory
• Liouville Quantum Gravity
• Random Planar Maps
• +7 more

Maxim Kontsevich has been a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS) since 1995, holding the AXA-IHES Chair for Mathematics . He is also Professor at Rutgers University (one month per year since 1997) and was Professor at University of California, Berkeley (1993–1995). Born 25 August 1964 in Khimki, former USSR, he became a French citizen in 1999. Education: Ph.D. in Mathematics, University of Bonn, March 1992. Research Interests: Prof. Kontsevich’s work lies at the intersection of algebraic geometry , mathematical physics , and quantum theory . He introduced revolutionary ideas in mirror symmetry , non-commutative geometry , and deformation quantization , creating new algebraic structures that have found applications far beyond their original contexts. His current ERC Synergy Grant “ReNew Quantum” (2019-2025) explores recursive and exact new quantum theory . Publications & Trends: Across more than 50 influential papers, Kontsevich has consistently pushed the boundaries of enumerative geometry , motivic integration , and topological field theory . His recent work delves into symplectic aspects of homological algebra , motivic Donaldson-Thomas invariants , non-archimedean geometry , and integrable systems , revealing deep connections between geometry, algebra, and physics. Scientific Awards & Honors: Fields Medal (1998) Crafoord Prize (2008) Shaw Prize in Mathematical Sciences (2012) Breakthrough Prize in Fundamental Physics (2012) Breakthrough Prize in Mathematics (2014) ERC Synergy Grant “ReNew Quantum” (2019) AMS Moore Prize (2025) Doctor Honoris Causa: Aarhus University (2014), Universität Wien (2015), Syddansk Universitet (2023) Member of Académie des Sciences, Institut de France, Academia Europaea, National Academy of Sciences (foreign), London Mathematical Society (honorary) Grants & Leadership: As Principal Investigator of the ERC Synergy Grant “ReNew Quantum” (€10 million, 2019-2025), Kontsevich coordinates an international team advancing exact methods and resurgence in quantum field and string theories. Editorial Service & Community Roles: He serves on the editorial boards of Compositio Mathematica , Publications Mathématiques IHÉS , Journal of Noncommutative Geometry , and several other leading journals, shaping the direction of contemporary mathematical research.

• Algebraic Geometry
• Mathematical Physics
• Mirror Symmetry
• +7 more

Jason P. Miller is a Professor in the Statistics Laboratory at the Department of Pure Mathematics and Mathematical Statistics (DPMMS), University of Cambridge, and a Fellow of Trinity College, Cambridge. He previously held the Poincaré Chair at IHP in the 2015-2016 academic year and was a post-doctoral researcher at MIT and Microsoft Research. Miller's research focuses on probability theory, particularly stochastic interface models, random surfaces, Schramm-Loewner evolutions (SLE), Liouville quantum gravity, and random planar maps. His work bridges mathematical physics and probability, exploring deep connections between random geometry, conformal field theory, and statistical mechanics. He has made fundamental contributions to understanding the relationship between Liouville quantum gravity and the Brownian map, and has extensively studied the properties of Schramm-Loewner evolutions in various contexts. Miller's publication record shows a consistent focus on the intersection of probability theory and mathematical physics, with a particular emphasis on scaling limits of discrete models to continuum objects. His work often involves collaborations with prominent researchers like Scott Sheffield and Ewain Gwynne, and demonstrates a progression from foundational work on SLE and the Gaussian free field to more recent breakthroughs in Liouville quantum gravity and its connections to random planar maps. Scientific Awards Rollo Davidson Prize, 2015 Poincaré Chair, 2015-2016 academic year Whitehead Prize, 2016 Clay Research Award, 2017 ICM invited speaker (probability and statistics), 2018 Doeblin Prize, 2018 Eisenbud Prize, 2023 Fermat Prize, 2023 Miller has supervised numerous PhD students (though specific names aren't listed in the provided text) and has been involved in significant research grants supporting his work in random geometry and probability theory. His editorial service includes positions on the boards of Probability Theory and Related Fields and Bernoulli journals. While specific laboratory details aren't provided, Miller's research appears to be theoretical in nature, focusing on mathematical analysis of random geometric structures. His work has significant implications for theoretical physics, particularly in understanding quantum gravity and critical phenomena in statistical mechanics.

• Probability Theory
• Stochastic Processes
• Schramm-Loewner Evolutions
• +7 more

Gregory F. Lawler is the George Wells Beadle Distinguished Service Professor in the Department of Mathematics at the University of Chicago. He also maintains appointments in the Department of Statistics and has affiliations with Computational and Applied Mathematics and Financial Mathematics programs. His academic background includes: B.A. (1976) from the University of Virginia Ph.D. (1979) from Princeton University under Edward Nelson Professor Lawler is a leading researcher in probability theory with a focus on conformally invariant processes , particularly the Schramm-Loewner Evolution (SLE) and various forms of random walks. His work bridges pure mathematics and statistical physics, establishing rigorous connections between discrete models and their continuous scaling limits. He has made fundamental contributions to understanding loop-erased random walks, Brownian motion, and the geometric properties of random curves, with applications in statistical mechanics for understanding two-dimensional critical phenomena. Analysis of his recent publications reveals a sustained focus on the mathematical foundations of SLE, with particular attention to natural parametrization, loop measures, convergence questions, and the relationship between discrete models and their continuous limits. His work consistently combines complex analysis with probabilistic methods to establish rigorous results about random curves. Professor Lawler is actively involved in mentoring through the University of Chicago's REU program and has developed extensive educational materials for students at all levels. His notes on probability theory and stochastic calculus are widely used resources within the mathematics community. He has authored several influential books including "Random Walk and the Heat Equation," "Conformally Invariant Processes in the Plane," and "Random Walk: A Modern Introduction" (with Vlada Limic), which have become standard references in probability theory.

• Probability Theory
• Random Walks
• Schramm-Loewner Evolution
• +3 more

Kyle Luh is an Assistant Professor at the University of Colorado Boulder in the Department of Mathematics, part of the College of Arts and Sciences. His research focuses on probability, random matrix theory, and randomized algorithms. Education: Ph.D. in Mathematics from Yale University (2017) His recent work explores eigenvalue gaps in random matrices, controllability of non-Hermitian systems, and applications to sparse reconstruction. Publications span topics like circular law for block band matrices, Littlewood–Offord inequalities, and stability analysis in quantum walks. Key trends in his research include spectral analysis of random graphs, robustness in learning algorithms, and combinatorial aspects of matrix theory. His articles highlight intersections between pure probability and applied computational methods.

• Probability
• Random Matrix Theory
• Randomized Algorithms
• +2 more

Dr. Yizheng Yuan is a Researcher in the Faculty of Mathematics at the University of Cambridge, affiliated with the Department of Pure Mathematics and Mathematical Statistics (DPMMS). His primary research focuses on Schramm-Loewner Evolution (SLE), stochastic processes, and conformal geometry. He has contributed to advancing understanding of SLE regularity properties, topological characterizations of Loewner traces, and support theorems for SLE curves. His work appears in prestigious journals such as Annales de l'Institut Henri Poincaré and Electronic Journal of Probability . Key research interests include probabilistic analysis of SLE paths, modulus of continuity estimates, and applications of stochastic differential equations in complex analysis. His studies bridge probability theory with mathematical physics, particularly in modeling random fractal curves and their geometric properties. Yuan's personal homepage is accessible at https://www.dpmms.cam.ac.uk/~yy547 , where further details on his research, preprints, and collaborations can be found. No awards or grants are explicitly listed in the provided text, though his publications reflect significant contributions to the field of probability and mathematical physics.

• Probability Theory
• Mathematical Physics
• Stochastic Processes
• +3 more

Jason Miller is a Reader in Probability at the Department of Pure Mathematics and Mathematical Statistics (DPMMS) within the Faculty of Mathematics at the University of Cambridge. His research focuses on advanced topics in probability theory and mathematical physics, particularly exploring the deep connections between random geometry, conformal invariance, and quantum gravity. Miller's research interests span a sophisticated range of topics in modern probability, with particular emphasis on Schramm-Loewner evolution (SLE), Gaussian free field, Liouville quantum gravity, random planar maps, and random walks. His work sits at the intersection of probability theory, complex analysis, and mathematical physics, developing rigorous mathematical frameworks for understanding two-dimensional random structures that arise in statistical mechanics and quantum gravity. He has made significant contributions to establishing the connections between discrete random structures and their continuum limits, particularly in the context of Liouville quantum gravity and the Brownian map. Analysis of Miller's recent publications reveals a consistent research program focused on establishing the deep connections between various mathematical objects in two-dimensional random geometry. His work demonstrates how Liouville quantum gravity serves as a universal scaling limit for random planar maps, how Schramm-Loewner evolution describes the continuum limits of critical interfaces, and how these objects relate to the Brownian map through various characterization theorems. The mathematical techniques employed span conformal field theory, metric geometry, stochastic analysis, and complex analysis. As a member of the Statistical Laboratory research group within DPMMS, Miller collaborates extensively with leading researchers in probability theory, including Scott Sheffield, Ewain Gwynne, and Wendelin Werner. His work has been published in the most prestigious mathematics journals including Acta Mathematica, Inventiones Mathematicae, and the Annals of Probability, reflecting the significance and rigor of his contributions to the field.

• Probability Theory
• Schramm-Loewner Evolution
• Gaussian Free Field
• +4 more

Michael Kozdron is an Associate Professor in the Department of Mathematics & Statistics at the University of Regina , with research focused on probability theory and stochastic processes. He holds a Ph.D. from Duke University (2004) and a B.Sc. from the University of British Columbia (1998). Education : B.Sc. (1998) - University of British Columbia Ph.D. (2004) - Duke University Research Interests : Probability theory and stochastic processes Schramm-Loewner evolution (SLE) Statistical mechanics Random walks and quantum probability Key Article Trends : 2022: Quantum martingales and convergence theorems 2016: Quantum random variables and spectral analysis 2013: SLE convergence rates and loop-erased walk dynamics 2012: Radial SLE Green's functions and quantum conditional expectation 2009-2007: SLE applications in Ising models and Fomin's identity 2005-2004: Excursion measures and planar random walk scaling Additional Activities : He supervises undergraduate and graduate students, maintains a Google Scholar profile , and shares simulations of random processes and lecture notes online.

• Probability Theory
• Stochastic Processes
• Schramm-Loewner Evolution
• +4 more

Gregory Markowsky serves as a Senior Lecturer in the School of Mathematics at Monash University, maintaining an active research profile with continuous publication output through 2025. His academic appointment shows no indication of part-time status, emeritus designation, or former staff classification. His research centers on three interconnected domains: Stochastic processes, particularly planar Brownian motion and random walk theory Complex analysis with applications to probabilistic models Graph theory focusing on algebraic and combinatorial structures These areas converge in his investigation of probabilistic phenomena with geometric interpretations. Recent publication trends reveal sustained productivity with 61 research outputs cataloged, including 4 articles in 2025 alone. His work demonstrates consistent methodological focus on stochastic analysis and combinatorial structures, with increasing cross-disciplinary applications in forensic science and econometrics as evidenced by 2024-2025 publications. Markowsky has secured three significant research projects funded by the Australian Research Council, including: "Planar Brownian motion and complex analysis" (2014-2017) as Primary Chief Investigator "Finite Markov chains in statistical mechanics and combinatorics" (2014-2017) "AMSI Industry Internship: Melbourne Storm" (2013) His ORCID profile (0000-0003-1656-337X) documents extensive scholarly activity with international collaborations. Professional engagement includes contributions toward UN Sustainable Development Goals through mathematical applications, though specific goal alignments aren't detailed in available materials. His email contact Greg.Markowsky@monash.edu remains active with current research dissemination.

• Stochastic processes
• Complex analysis
• Graph theory

Nathanael Berestycki is a University Professor (Univ.-Prof.) in the Department of Mathematics within the Faculty of Mathematics. His research spans multiple areas of probability theory and mathematical physics with a particular focus on stochastic processes and their connections to statistical mechanics and quantum gravity. Professor Berestycki's research interests center around probability theory, with significant contributions to the understanding of Gaussian free fields, Liouville quantum gravity, and random processes. His work explores deep connections between statistical mechanics and mathematical physics, particularly in the context of conformal invariance and scaling limits. He has made substantial contributions to the theory of dimers, Brownian motion, random graphs, and branching processes, often revealing unexpected connections between seemingly disparate areas of mathematics. Analysis of his recent publications shows a consistent focus on the intersection of probability theory and mathematical physics, with particular emphasis on conformal invariance properties, scaling limits of discrete models, and the mathematical structure of quantum gravity. His work often bridges theoretical developments with concrete applications in statistical mechanics, demonstrating how deep mathematical structures emerge from seemingly simple probabilistic models. The breadth of his research is reflected in publications across top probability and mathematical physics journals. Throughout his career, Berestycki has maintained a high level of productivity with consistent publication output across leading journals in probability theory and mathematical physics. His collaborative work with researchers across institutions demonstrates strong connections within the mathematical community, particularly in the European probability research network.

• Probability Theory
• Statistical Mechanics
• Mathematical Physics
• +8 more

Fredrik Viklund is a Professor at the Department of Mathematics, KTH Royal Institute of Technology. He holds the Wallenberg Scholar title and receives research funding from the Swedish Research Council (VR) and the Gustafson Foundation. His research focuses on the intersection of complex analysis, probability, and mathematical physics, with applications to computer science and applied mathematics. PhD from KTH Simons Fellow and J.F. Ritt Assistant Professor at Columbia University Associate Professor at Uppsala University Research interests include: Schramm-Loewner evolution (SLE) curves Critical lattice models Laplacian growth and aggregation Conformal field theory Teichmüller theory Gaussian fields Recent publications focus on Coulomb gases, Loewner energy, Hele-Shaw flows, and lattice Yang-Mills theories. Notably, his work explores the interplay between Loewner chains and Dirichlet energies. Scientific roles: Editorial Board: Arkiv för Matematik and Analysis and Mathematical Physics Scientific Council for Natural and Engineering Sciences, Swedish Research Council (VR) Member of the Random Matrix Theory and Random Geometry (RMRG) research group Advising: Supervises PhD students and collaborates with postdocs. Organizes the KTH Probability and Mathematical Physics Seminar.

• Complex Analysis
• Probability Theory
• Mathematical Physics
• +9 more

Dr. Jan Swart is a Professor at the Department of Probability and Mathematical Statistics within the Faculty of Mathematics and Physics at Charles University, and a researcher at the Institute of Information Theory and Automation (UTIA) of The Czech Academy of Sciences in Prague. His office is located at Pod vodarenskou vezi 4, 18200 Praha 8, Czech Republic, where he works in Room 112 of the Stochastic Informatics department. Professor Swart specializes in probability theory with particular expertise in interacting particle systems, stochastic processes, and their mathematical foundations. His research spans quantum probability, random matrix theory, Markov chains, large deviations, and Brownian continuum objects. He has developed significant theoretical frameworks for understanding complex stochastic systems and their scaling limits. His publication record shows a consistent focus on advancing the mathematical understanding of interacting systems, with lecture notes and research materials that have become valuable resources in the field. His work demonstrates strong connections between theoretical probability and applications in statistical physics and theoretical biology. Professor Swart has supervised numerous theses and taught a wide range of advanced courses including Quantum Probability Theory, Interacting Particle Systems, Random Matrix Theory, and Advanced Markov Chains. He has also created a comprehensive simulation library for interacting particle systems that enables numerical exploration of these complex models. Notably, Professor Swart has also contributed to mathematical education through creative works including a mathematical fairy tale titled "Roulette a la princess" that explores game theory and probability concepts in an engaging narrative format. His work on the Czech language demonstrates his integration into the local academic community while maintaining international scholarly connections.

• Probability Theory
• Mathematical Statistics
• Interacting Particle Systems
• +5 more