Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics, is a one-day event for the benefit of the greater Boston area mathematics community.<\/p>\n\n\n\n\n\n
9:30 a.m \u2013 9:50 a.m.
\nRegistration and Coffee<\/p>\n
9:50 a.m. \u2013 10:00 a.m.
\nOpening Remarks<\/p>\n
10:00 a.m. \u2013 11:00 a.m.
\nTalk 1: Yuval Peres, Microsoft Research<\/p>\n
11:10 a.m. \u2013 12:10 p.m.
\nTalk 2: Irit Dinur, Weizmann Institute of Science<\/p>\n
12:10 p.m. \u2013 1:40 p.m.
\nLunch Break<\/p>\n
1:40 p.m. \u2013 2:40 p.m.
\nTalk 3: Persi Diaconis, Stanford University<\/p>\n
2:50 p.m. \u2013 3:50 p.m.
\nTalk 4: Alice Guionnet, Massachusetts Institute of Technology<\/p>\n
3:50 p.m. \u2013 4:20 p.m.
\nAfternoon Break<\/p>\n
4:20 p.m. \u2013 5:20 p.m.
\nTalk 5: Gerard Ben Arous, New York University<\/p>\n\n\n\n\n\n
\n<\/p>
Yuval Peres, Microsoft Research<\/p>\n
A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1928); we find a new connection to game theory and probability. A hunter and a rabbit move on the integer points in [0,n) without seeing each other. At each step, the hunter moves to a neighboring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. The known optimal randomized strategies for hunter and rabbit achieve expected capture time of order n log n. We show that every rabbit strategy yields a Kakeya set; the optimal rabbit strategy is based on a discretized Cauchy random walk, and it yields a Kakeya set K consisting of 4n triangles, that has minimal area among such sets (the area of K is of order 1\/log(n)). Passing to the scaling limit yields a simple construction of a random Kakeya set with zero area from two Brownian motions. (Joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler).<\/p>\n
<\/p><\/div>\n
\n<\/p>
Irit Dinur, Weizmann Institute of Science<\/p>\n
Probabilistically checkable proofs (PCPs) are proofs in which the distance between right and wrong is greatly amplified: a verifier needs read only O(1) bits of the proof to make its decision. A PCP can be constructed by pushing any proof through a gap-amplifying transformation. One of the most basic ways to get gap-amplification is by parallel repetition, aka direct product. This is a very easy-to-define operation, yet its analysis leaves many open questions. We will introduce PCPs and direct products and then survey existing results and describe some open questions.<\/p>\n
<\/p><\/div>\n
\n<\/p>
Persi Diaconis, Stanford University<\/p>\n
The study of \u201ccarries\u201d when we add numbers has surprisingly rich connections with probability and parts of algebra (work with Borodin and Fulman). Simple changes, e.g., using \u201cbalanced arithmetic,\u201d lead to new problems. In joint work with Haow and Soundararajan, we show how additive combinatorics (Freiman, Szemeredi) saves the day.<\/p>\n
<\/p><\/div>\n
\n<\/p>
Alice Guionnet, Massachusetts Institute of Technology<\/p>\n
During the last twenty years, the theory of mass transportation and optimal transport was shown to have many applications in diverse fields of mathematics. In this talk, we will discuss its first generalization to a non-commutative setting as well as its applications to derive isomorphisms of some C* algebras. We will introduce some basics of the theory of optimal transport as well as of free probability, the natural set up for such a generalization. This is joint work with D. Shlyakhtenko.<\/p>\n
<\/p><\/div>\n
\n<\/p>
Gerard Ben Arous, New York University<\/p>\n
Abstract TBD<\/p>\n
<\/p><\/div>\n
<\/p><\/div>\n\n\n\n\n\n
Alice Guionnet<\/a>, Massachusetts Institute of Technology Alexei Borodin (MIT), Ivan Corwin (Clay Mathematics Institute and MIT), Yashodhan Kanoria (Microsoft Research), Jason Miller (MIT), Scott Sheffield (MIT) and H.T. Yau (Harvard University).<\/p>\n\n\n","protected":false},"excerpt":{"rendered":" Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics, is a one-day event for the benefit of the greater Boston area mathematics community.<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"msr_startdate":"2012-10-05","msr_enddate":"","msr_location":"","msr_expirationdate":"","msr_event_recording_link":"","msr_event_link":"","msr_event_link_redirect":false,"msr_event_time":"","msr_hide_region":false,"msr_private_event":true,"footnotes":""},"research-area":[13561,13546],"msr-region":[],"msr-event-type":[],"msr-video-type":[],"msr-locale":[268875],"msr-program-audience":[],"msr-post-option":[],"msr-impact-theme":[],"class_list":["post-286760","msr-event","type-msr-event","status-publish","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-locale-en_us"],"msr_about":"\n\n\n\n\n Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics, is a one-day event for the benefit of the greater Boston area mathematics community.<\/p>\n\n\n\n\n\n 9:30 a.m \u2013 9:50 a.m. 9:50 a.m. \u2013 10:00 a.m. 10:00 a.m. \u2013 11:00 a.m. 11:10 a.m. \u2013 12:10 p.m. 12:10 p.m. \u2013 1:40 p.m. 1:40 p.m. \u2013 2:40 p.m. 2:50 p.m. \u2013 3:50 p.m. 3:50 p.m. \u2013 4:20 p.m. 4:20 p.m. \u2013 5:20 p.m. \n<\/p> Yuval Peres, Microsoft Research<\/p>\n A planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1928); we find a new connection to game theory and probability. A hunter and a rabbit move on the integer points in [0,n) without seeing each other. At each step, the hunter moves to a neighboring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. The known optimal randomized strategies for hunter and rabbit achieve expected capture time of order n log n. We show that every rabbit strategy yields a Kakeya set; the optimal rabbit strategy is based on a discretized Cauchy random walk, and it yields a Kakeya set K consisting of 4n triangles, that has minimal area among such sets (the area of K is of order 1\/log(n)). Passing to the scaling limit yields a simple construction of a random Kakeya set with zero area from two Brownian motions. (Joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler).<\/p>\n <\/p><\/div>\n \n<\/p> Irit Dinur, Weizmann Institute of Science<\/p>\n Probabilistically checkable proofs (PCPs) are proofs in which the distance between right and wrong is greatly amplified: a verifier needs read only O(1) bits of the proof to make its decision. A PCP can be constructed by pushing any proof through a gap-amplifying transformation. One of the most basic ways to get gap-amplification is by parallel repetition, aka direct product. This is a very easy-to-define operation, yet its analysis leaves many open questions. We will introduce PCPs and direct products and then survey existing results and describe some open questions.<\/p>\n <\/p><\/div>\n \n<\/p> Persi Diaconis, Stanford University<\/p>\n The study of \u201ccarries\u201d when we add numbers has surprisingly rich connections with probability and parts of algebra (work with Borodin and Fulman). Simple changes, e.g., using \u201cbalanced arithmetic,\u201d lead to new problems. In joint work with Haow and Soundararajan, we show how additive combinatorics (Freiman, Szemeredi) saves the day.<\/p>\n <\/p><\/div>\n \n<\/p> Alice Guionnet, Massachusetts Institute of Technology<\/p>\n During the last twenty years, the theory of mass transportation and optimal transport was shown to have many applications in diverse fields of mathematics. In this talk, we will discuss its first generalization to a non-commutative setting as well as its applications to derive isomorphisms of some C* algebras. We will introduce some basics of the theory of optimal transport as well as of free probability, the natural set up for such a generalization. This is joint work with D. Shlyakhtenko.<\/p>\n <\/p><\/div>\n \n<\/p> Gerard Ben Arous, New York University<\/p>\n Abstract TBD<\/p>\n <\/p><\/div>\n <\/p><\/div>\n\n\n\n\n\n Alice Guionnet<\/a>, Massachusetts Institute of Technology Alexei Borodin (MIT), Ivan Corwin (Clay Mathematics Institute and MIT), Yashodhan Kanoria (Microsoft Research), Jason Miller (MIT), Scott Sheffield (MIT) and H.T. Yau (Harvard University).<\/p>\n\n\n","tab-content":[{"id":0,"name":"About","content":"Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics, is a one-day event for the benefit of the greater Boston area mathematics community."},{"id":1,"name":"Agenda","content":"9:30 a.m - 9:50 a.m.\r\nRegistration and Coffee\r\n\r\n9:50 a.m. - 10:00 a.m.\r\nOpening Remarks\r\n\r\n10:00 a.m. - 11:00 a.m.\r\nTalk 1: Yuval Peres, Microsoft Research\r\n\r\n11:10 a.m. - 12:10 p.m.\r\nTalk 2: Irit Dinur, Weizmann Institute of Science\r\n\r\n12:10 p.m. - 1:40 p.m.\r\nLunch Break\r\n\r\n1:40 p.m. - 2:40 p.m.\r\nTalk 3: Persi Diaconis, Stanford University\r\n\r\n2:50 p.m. - 3:50 p.m.\r\nTalk 4: Alice Guionnet, Massachusetts Institute of Technology\r\n\r\n3:50 p.m. - 4:20 p.m.\r\nAfternoon Break\r\n\r\n4:20 p.m. - 5:20 p.m.\r\nTalk 5: Gerard Ben Arous, New York University"},{"id":2,"name":"Abstracts","content":"\r\n[accordion]\r\n\r\n[panel header=\"Talk 1: Hunter, Cauchy Rabbit, and Optimal Kakeya Sets\"]\r\nYuval Peres, Microsoft Research\r\n\r\nA planar set that contains a unit segment in every direction is called a Kakeya set. These sets have been studied intensively in geometric measure theory and harmonic analysis since the work of Besicovich (1928); we find a new connection to game theory and probability. A hunter and a rabbit move on the integer points in [0,n) without seeing each other. At each step, the hunter moves to a neighboring vertex or stays in place, while the rabbit is free to jump to any node. Thus they are engaged in a zero sum game, where the payoff is the capture time. The known optimal randomized strategies for hunter and rabbit achieve expected capture time of order n log n. We show that every rabbit strategy yields a Kakeya set; the optimal rabbit strategy is based on a discretized Cauchy random walk, and it yields a Kakeya set K consisting of 4n triangles, that has minimal area among such sets (the area of K is of order 1\/log(n)). Passing to the scaling limit yields a simple construction of a random Kakeya set with zero area from two Brownian motions. (Joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler).\r\n[\/panel]\r\n\r\n[panel header=\"Talk 2: Direct Products and Gap Amplification\"]\r\nIrit Dinur, Weizmann Institute of Science\r\n\r\nProbabilistically checkable proofs (PCPs) are proofs in which the distance between right and wrong is greatly amplified: a verifier needs read only O(1) bits of the proof to make its decision. A PCP can be constructed by pushing any proof through a gap-amplifying transformation. One of the most basic ways to get gap-amplification is by parallel repetition, aka direct product. This is a very easy-to-define operation, yet its analysis leaves many open questions. We will introduce PCPs and direct products and then survey existing results and describe some open questions.\r\n[\/panel]\r\n\r\n[panel header=\"Talk 3: Probability and additive Combinatorics\"]\r\nPersi Diaconis, Stanford University\r\n\r\nThe study of \"carries\" when we add numbers has surprisingly rich connections with probability and parts of algebra (work with Borodin and Fulman). Simple changes, e.g., using \"balanced arithmetic,\" lead to new problems. In joint work with Haow and Soundararajan, we show how additive combinatorics (Freiman, Szemeredi) saves the day.\r\n[\/panel]\r\n\r\n[panel header=\"Talk 4: Free Monotone Transport\"]\r\nAlice Guionnet, Massachusetts Institute of Technology\r\n\r\nDuring the last twenty years, the theory of mass transportation and optimal transport was shown to have many applications in diverse fields of mathematics. In this talk, we will discuss its first generalization to a non-commutative setting as well as its applications to derive isomorphisms of some C* algebras. We will introduce some basics of the theory of optimal transport as well as of free probability, the natural set up for such a generalization. This is joint work with D. Shlyakhtenko.\r\n[\/panel]\r\n\r\n[panel header=\"Talk 5: TBD\"]\r\nGerard Ben Arous, New York University\r\n\r\nAbstract TBD\r\n[\/panel]\r\n\r\n[\/accordion]"},{"id":3,"name":"People","content":"Alice Guionnet<\/a>, Massachusetts Institute of Technology\r\nGerard Ben Arous<\/a>, New York University\r\nIrit Dinur<\/a>, Weizmann Institute of Science\r\nPersi Diaconis<\/a>, Stanford University\r\nYuval Peres<\/a>, Microsoft Research\r\n\r\nAlexei Borodin (MIT), Ivan Corwin (Clay Mathematics Institute and MIT), Yashodhan Kanoria (Microsoft Research), Jason Miller (MIT), Scott Sheffield (MIT) and H.T. Yau (Harvard University)."}],"msr_startdate":"2012-10-05","msr_enddate":"","msr_event_time":"","msr_location":"","msr_event_link":"","msr_event_recording_link":"","msr_startdate_formatted":"October 5, 2012","msr_register_text":"Watch now","msr_cta_link":"","msr_cta_text":"","msr_cta_bi_name":"","featured_image_thumbnail":null,"event_excerpt":"Jointly organized by Harvard University, Massachusetts Institute of Technology, and Microsoft Research New England, the Charles River Lectures on Probability and Related Topics, is a one-day event for the benefit of the greater Boston area mathematics community.","msr_research_lab":[199563],"related-researchers":[],"msr_impact_theme":[],"related-academic-programs":[],"related-groups":[],"related-projects":[],"related-opportunities":[],"related-publications":[],"related-videos":[],"related-posts":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-event\/286760"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-event"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-event"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-event\/286760\/revisions"}],"predecessor-version":[{"id":874464,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-event\/286760\/revisions\/874464"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=286760"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=286760"},{"taxonomy":"msr-region","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-region?post=286760"},{"taxonomy":"msr-event-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-event-type?post=286760"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=286760"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=286760"},{"taxonomy":"msr-program-audience","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-program-audience?post=286760"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=286760"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=286760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nGerard Ben Arous<\/a>, New York University
\nIrit Dinur<\/a>, Weizmann Institute of Science
\nPersi Diaconis<\/a>, Stanford University
\nYuval Peres<\/a>, Microsoft Research<\/p>\n
\nRegistration and Coffee<\/p>\n
\nOpening Remarks<\/p>\n
\nTalk 1: Yuval Peres, Microsoft Research<\/p>\n
\nTalk 2: Irit Dinur, Weizmann Institute of Science<\/p>\n
\nLunch Break<\/p>\n
\nTalk 3: Persi Diaconis, Stanford University<\/p>\n
\nTalk 4: Alice Guionnet, Massachusetts Institute of Technology<\/p>\n
\nAfternoon Break<\/p>\n
\nTalk 5: Gerard Ben Arous, New York University<\/p>\n\n\n\n\n\n\n\t\t\t\tTalk 1: Hunter, Cauchy Rabbit, and Optimal Kakeya Sets\t\t\t<\/h4>\n
\n\t\t\t\tTalk 2: Direct Products and Gap Amplification\t\t\t<\/h4>\n
\n\t\t\t\tTalk 3: Probability and additive Combinatorics\t\t\t<\/h4>\n
\n\t\t\t\tTalk 4: Free Monotone Transport\t\t\t<\/h4>\n
\n\t\t\t\tTalk 5: TBD\t\t\t<\/h4>\n
\nGerard Ben Arous<\/a>, New York University
\nIrit Dinur<\/a>, Weizmann Institute of Science
\nPersi Diaconis<\/a>, Stanford University
\nYuval Peres<\/a>, Microsoft Research<\/p>\n