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Dear all, The first Analysis and Probability seminar of the semester will be held this Friday at 1:30 PM in MONT 313. The speaker is Robert Neel from Lehigh University. The title of his talk is "Geometric and Martin boundaries on Cartan-Hadamard manifolds," and the abstract is below. I will send a reminder email before the talk, and future announcement emails will be sent on Friday mornings. You can find information about future A/P talks here: http://calendar.uconn.edu/2019/month/09/376/<https://nam01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fcalendar.uconn.edu%2F2019%2Fmonth%2F09%2F376%2F&data=02%7C01%7C%7C2cb083ebf06d4a4b650508d740884cdd%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C637048826500367291&sdata=D5p5Tbq%2BQgZrQf0IeGmZdrLH2z27RXo3hCA1Pp2HGew%3D&reserved=0>. Best, Scott Abstract: We recall results on the solvability of the Dirichlet problem at infinity (DPI) and the identification of the geometric and Martin boundaries for Cartan-Hadamard manifolds, by both stochastic and non-stochastic methods. The situation is rather different in the two-dimensional and higher-dimensional cases. In the two-dimensional case, by studying the long-time behavior of Brownian motion, we give a condition for the solvability of the DPI that is flexible enough to allow for flats and moreover, also shows that any upper radial curvature bound yielding transience also yields solvability of the DPI. We then indicate what solvability of the DPI implies for the relationship between the geometric boundary and the Martin boundary in dimension 2. Finally, under “matched” upper and lower curvature bounds, which are weaker than those known in higher dimensions (in recent work of Ran Ji), we show that the Martin boundary is naturally homeomorphic to the sphere at infinity. Scott Zimmerman, PhD | Assistant Research Professor Department of Mathematics | University of Connecticut