Date | Time | Room | Title |
---|---|---|---|

Monday, April 22, 2013 |
4:00-5:00 pm | DUAN G1B20 |
Laplacian Growth and the Mystery of the Abelian Sandpile: a Visual TourWe compare several growth models on the two dimensional lattice. In some models, like internal DLA and rotor-router aggregation, the scaling limits are universal; in particular, starting from a point source yields a disk. In the abelian sandpile, particles are added at the origin and whenever a site has four particles or more, the top four particles topple, with one going to each neighbor. Despite similarities to other models, for the sandpile, the intriguing pattern that arises is not circular and depends on the particular lattice. A scaling limit exists for the sandpile, as was recently shown by Pegden and Smart, but it is not universal and is still mysterious. This research has been greatly influenced by pictures of the relevant sets, which I will show in the talk. They suggest a connection to conformal mapping which has not been established yet. (Talk based on joint works with Lionel Levine.) Following Monday's lecture, there will be a reception in honor of Professor Peres at the Koenig Alumni Center, 1202 University Avenue (the SE corner of Broadway and University). |

Tuesday, April 23, 2013 |
4:00-5:00 pm | DUAN G1B20 |
Hunter, Cauchy Rabbit, and Optimal Kakeya SetsA 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 an n-vertex cycle without seeing each other until they meet. 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. 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 Kakeya 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.) |

## Yuval Peres |
Yuval Peres is a Principal Researcher in the Theory group at Microsoft Research. Before joining MSR in 2006, he was a Professor at UC Berkeley. He has also taught at Yale and at the Hebrew University. Yuval has published more than 200 papers with 100 co-authors and has mentored 19 PhD theses. His research encompasses many areas of probability theory, including random walks, Brownian motion, percolation, point processes and random graphs as well as connections with Ergodic Theory, PDEs, Combinatorics, Fractals, and Theoretical Computer Science. He has recently co-authored books on Markov chains and mixing times, on zeros of Gaussian analytic functions, and on Brownian motion. Yuval is a fellow of the AMS and a recipient of the Rollo Davidson Prize. In 2001 he received the Loeve Prize, awarded once every two years to a leading probabilist. Yuval was an invited speaker at the International Congress of Mathematics (2002) and in the European Congress of Mathematics (2008). His favorite quote is from his son Alon, who was overheard at age 6 asking a friend: "Leo, do you have a religion? You know, a religion, like Christian, or Jewish, or Mathematics....?" |

This Lecture Series is funded by an endowment given by Professor Ira M. DeLong, who came to the University of Colorado in 1888 at the age of 33. Professor DeLong essentially became the mathematics department by teaching not only the college subjects but also the preparatory mathematics courses. Professor DeLong was a prominent citizen of the community of Boulder as well as president of the Mercantile Bank and Trust Company, organizer of the Colorado Education Association, and president of the charter convention that gave Boulder the city manager form of government in 1917. After his death in 1942 it was decided that the bequest he made to the mathematics department would accumulate interest until income became available to fund DeLong prizes for undergraduates and DeLong Lectureships to bring outstanding mathematicians to campus each year. The first DeLong Lectures were delivered in the 1962-63 academic year.

1962-1963 Paul Halmos

1963-1964 Marshall Hall Jr.

1964-1965 Edwin Hewitt

1965-1966 George Polya

1966-1967 Alfred Tarski

1967-1968 John Milnor

1968-1969 Paul Cohen

1969-1970 Jurgen Moser

1970-1971 Mark Kac, Irving Kaplansky

1971-1972 Abraham Robinson

1972-1973 George Mackey

1973-1974 Olga Taussky Todd

1974-1975 Andrew Gleason

1975-1976 Tosio Kato

1976-1977 Hugh Montgomery

1977-1978 Elias Stein

1978-1979 Raoul Bott

1979-1980 Alan Weinstein

1980-1981 Enrico Bombieri

1981-1982 Richard S. Varga

1963-1964 Marshall Hall Jr.

1964-1965 Edwin Hewitt

1965-1966 George Polya

1966-1967 Alfred Tarski

1967-1968 John Milnor

1968-1969 Paul Cohen

1969-1970 Jurgen Moser

1970-1971 Mark Kac, Irving Kaplansky

1971-1972 Abraham Robinson

1972-1973 George Mackey

1973-1974 Olga Taussky Todd

1974-1975 Andrew Gleason

1975-1976 Tosio Kato

1976-1977 Hugh Montgomery

1977-1978 Elias Stein

1978-1979 Raoul Bott

1979-1980 Alan Weinstein

1980-1981 Enrico Bombieri

1981-1982 Richard S. Varga

1982-1983 Charles Fefferman

1983-1984 S.S. Chern

1984-1985 Robert Zimmer

1985-1986 Gerd Faltings

1986-1987 Dennis Sullivan

1987-1988 Stephen Smale

1988-1989 Branko Grunbaum

1989-1990 Ronald Graham

1990-1991 Kenneth Ribet

1991-1992 Michael Atiyah

1992-1993 John H. Conway

1993-1994 John Tate

1994-1995 Vladimir Arnold

1996-1997 Alain Connes

1997-1998 Barry Mazur

1999-2000 Nigel Higson

2000-2001 Jeff Cheeger

2001-2002 Vaughan F. R. Jones

2002-2003 Richard Taylor

2003-2004 Phillip A. Griffiths

1983-1984 S.S. Chern

1984-1985 Robert Zimmer

1985-1986 Gerd Faltings

1986-1987 Dennis Sullivan

1987-1988 Stephen Smale

1988-1989 Branko Grunbaum

1989-1990 Ronald Graham

1990-1991 Kenneth Ribet

1991-1992 Michael Atiyah

1992-1993 John H. Conway

1993-1994 John Tate

1994-1995 Vladimir Arnold

1996-1997 Alain Connes

1997-1998 Barry Mazur

1999-2000 Nigel Higson

2000-2001 Jeff Cheeger

2001-2002 Vaughan F. R. Jones

2002-2003 Richard Taylor

2003-2004 Phillip A. Griffiths

2004-2005 Paul Baum

2005-2006 Isadore M. Singer

2006-2007 Sir Roger Penrose

2007-2008 Maxim Kontsevich

2008-2009 Persi Diaconis

2009-2010 Ieke Moerdijk

2010-2011 Endre Szemerédi

2011-2012 Vitaly Bergelson

2012-2013 Yuval Peres

2013-2014 Benedict H. Gross

2014-2015 Robert Bryant

2015-2016 Magdalena Musat

2017-2018 Michael J. Hopkins

2005-2006 Isadore M. Singer

2006-2007 Sir Roger Penrose

2007-2008 Maxim Kontsevich

2008-2009 Persi Diaconis

2009-2010 Ieke Moerdijk

2010-2011 Endre Szemerédi

2011-2012 Vitaly Bergelson

2012-2013 Yuval Peres

2013-2014 Benedict H. Gross

2014-2015 Robert Bryant

2015-2016 Magdalena Musat

2017-2018 Michael J. Hopkins

If you have any questions concerning this lecture series, please contact
Mathematics.