جست‌وجوی استاد و پژوهشگر

James Proppمشاهده پروفایل

استاد

• Combinatorics
• Probability
• Dynamical Systems

James Propp, Ph.D., is a Professor in the Department of Mathematics & Statistics at the University of Massachusetts Lowell (Kennedy College of Sciences). He specializes in Combinatorics, Probability, and Dynamical Systems. His work bridges theoretical mathematics with applications in discrete structures and algorithmic processes. Propp has been actively mentoring undergraduates in research since joining UMass Lowell in 2006. Education: Ph.D., University of California at Berkeley Research Interests: Propp’s research focuses on tilings of geometric structures (e.g., Aztec diamonds, benzels), combinatorial dynamics, and homomesy phenomena. He explores probabilistic models in discrete systems and develops bijections for enumeration problems. His work often combines algebraic, geometric, and computational approaches. Recent Research Trends: Propp’s recent publications highlight advancements in tiling theory, toggle dynamics, and spectral analysis of combinatorial systems. His work on homomesy elucidates invariant averages under dynamical actions, while his studies on chip-firing games and rotor-routers model probabilistic phenomena deterministically. Awards: No awards explicitly mentioned in the text. Advising & Grants: While no specific grants are listed, Propp is noted for encouraging undergraduate research participation in mathematics. His advising contributions are central to his role as a mentor. Labs/Teams: No specific labs or collaborative teams are detailed in the provided information.

• Probability Theory
• Discrete Probability
• Random Planar Maps
• +۶ مورد دیگر

Daniel C. Jerison is an Assistant Professor in the Department of Mathematics and Statistics at the University of San Francisco, supporting undergraduate programs in mathematics and data science. His academic career demonstrates a strong trajectory through prestigious institutions including Stanford University, Harvard University, Cornell University, and Tel Aviv University. Education: PhD in Mathematics, Stanford University, 2016 BA in Mathematics, Harvard University, 2007 Dr. Jerison specializes in discrete probability theory with emphasis on the properties of random objects and convergence of Markov chain algorithms. His research explores random planar maps, abelian sandpiles, circle packing, and discrete complex analysis. His work bridges theoretical mathematics with applications in statistical physics, examining how complex systems evolve and reach equilibrium states through sophisticated probabilistic methods. His approach often combines combinatorial techniques with analytical methods to solve problems in discrete geometry and probability. Analysis of Dr. Jerison's publications reveals consistent focus on the intersection of probability theory and discrete structures. His research demonstrates sophisticated mathematical techniques for analyzing convergence rates in Markov chains, establishing geometric criteria for planar structures, and solving boundary value problems for discrete systems. The recurring themes across his work include probabilistic methods applied to geometric problems, the study of self-organized critical systems, and theoretical frameworks for understanding complex discrete phenomena. Dr. Jerison has extensive teaching experience across multiple institutions, teaching courses ranging from foundational calculus to advanced probability theory. He has taught Probability Theory I (Math 6710), Stochastic Processes (Math 4740), Linear Algebra for Engineers (Math 2940), Prove It! (Math 3040), and Applied Complex Analysis (Math 4220) at Cornell University, in addition to his current teaching responsibilities at USF. He has also been involved with prestigious summer programs for high school students including PROMYS and SUMaC, where he directed research labs and served on admission committees.

• Probability Theory
• Discrete Probability
• Markov Chains
• +۶ مورد دیگر

Daniel Jerison is an Assistant Professor in the Department of Mathematics and Statistics at the University of San Francisco, where he supports undergraduate programs in mathematics and data science. He holds a PhD in Mathematics from Stanford University (2016) and a BA in Mathematics from Harvard University (2007). His educational background includes: PhD in Mathematics, Stanford University, 2016 BA in Mathematics, Harvard University, 2007 Professor Jerison specializes in discrete probability theory, with research focusing on circle packing and discrete complex analysis, abelian sandpile and rotor-router models, and Markov chain convergence and mixing times. His work bridges theoretical mathematics with applications in statistical physics and computer science. His research demonstrates a consistent trajectory toward understanding the properties of random objects and stochastic processes, particularly in discrete settings where traditional continuous methods face challenges. His scholarly contributions include publications in prestigious journals such as Advances in Mathematics, Communications in Mathematical Physics, and Transactions of the American Mathematical Society, reflecting his significant contributions to the field of probability theory. Professor Jerison has been actively involved in teaching a wide range of mathematics courses including probability theory, stochastic processes, complex analysis, and linear algebra. He has also contributed to mathematics education through involvement with PROMYS and SUMaC, summer programs for high school students, where he directed research labs and served on admission committees. His academic journey includes postdoctoral positions at Cornell University working with Lionel Levine and at Tel Aviv University under Asaf Nachmias, establishing him within a strong network of researchers in probability theory and discrete mathematics.