THURSDAY, APRIL 5
- ESB 6.110, 12:00 p.m.
- MATH - PHYSICS (BCDE) LUNCH SEMINAR
- Dr. Per Berglund, CITUSC Center for Theoretical Physics, University of South California, Los Angeles
- Stability of Vector Bundles from F-theory
- 241 Altgeld Hall, 1:00 p.m.
- ANALYTIC NUMBER THEORY
- Professor Gwyn Coogan, University of Wisconsin, Madison
- Generating functions for certain L-series values
- Abstract: In recent papers D. Zagier and Andrews, Ono, and
Jimenez-Urroz explored the q-series identities which result when one
considers the 'sum of tails' of certain modular forms. In some cases
they were able to produce the generating functions for the values of
L-series at negative integers. We have found that generating functions
of this type are widespread and follow naturally from an analysis,
which does not involve the 'sum of tails', of a single variable theta
identity, which is similar the the Jacobi Triple Product Identity.
- 347 Altgeld Hall, 1:00 p.m.
- GROUP THEORY SEMINAR
- Professor Yevgeniy Gordon
- Quantum computations and problems in group theory
- 241 Altgeld Hall, 2:00 p.m.
- ALGEBRAIC GROUPS AND THEIR REPRESENTATIONS
- Frobenius Splitting of Sehubert Cells
- 243 Altgeld Hall, 2:00 p.m.
- JOINT ANALYTIC/ALGEBRAIC NUMBER THEORY
- Professor Jeremy Lovejoy, University of Wisconsin, Madison
- Modular Forms and Arithmetic Properties of Partition Functions
- Abstract: There are many natural questions about partition functions
which are unattackable using combinatorial techniques or
methods from classical analytic number theory. Here we survey
some of these questions, explain why the theory of modular
forms is relevant, and give a sample of the fascinating results
which we now can obtain.
- 347 Altgeld Hall, 2:00 p.m.
- ANALYSIS SEMINAR
- Professor Anthony G. O'Farrell, National University of Ireland, Maynooth
- Pervasive spaces of analytic functions
- Abstract:We describe those open sets U in the sphere such that
A(U) is pervasive, and those such that the set of real
parts of elements of A(U) is pervasive.
A(U) means the uniform algebra of all functions continuous
the closure of U and holomorphic on the interior of U.
Pervasive means (roughly) that when you remove any nonempty
relatively open piece of the boundary of U, then you can approximate
all complex-valued (resp. real-valued) functions
on the rest of the boundary, uniformly by elements of
A(U) (resp. Re A(U)).
- 141 CSRL, 2:30 p.m.
- DECISION, CONTROL, AND OPTIMIZATION SEMINAR
- Rene Vidal, Electrical Engineering and Computer Science Department, University of California, Berkeley, Berkeley, California
- Multi-Agent Probabilistic Pursuit-Evasion Games with Unmanned
Ground and Aerial Vehicles
- Abstract: We consider the problem of having a team of Unmanned Ground
Vehicles (UGV) and Unmanned Aerial Vehicles (UAV) pursue a second team
of evaders while concurrently building a map in an unknown
environment. We cast the problem in a probabilistic game theoretic
framework and consider two computationally feasible pursuit policies:
greedy and global-max. To implement this scenario on real UAVs and
UGVs, we propose a distributed hierarchical hybrid system architecture
which emphasizes the autonomy of each agent yet allows for coordinated
team efforts. We then describe our implementation on a fleet of UGVs
and UAVs, detailing components such as high level pursuit policy
computation, inter-agent communication, navigation, sensing, and
control. We present both simulation and experimental results on real
pursuit-evasion games between our fleet of UAVs and UGVs and evaluate
the pursuit policies relating expected capture times to the speed and
intelligence of the evaders and the sensing capabilities of the
pursuers.
- NOTE: Coffee and cookies at 2:10 p.m. before the seminar in Room 154 CSRL.
- 145 Altgeld Hall, 3:00 p.m.
- COLORING THEORY RESEARCH GROUP
- Discussion of open problems
- 243 Altgeld Hall, 3:00 p.m.
- COMMUTATIVE RING THEORY RAP
- Professor Phillip Griffith, Department of Mathematics, UIUC
- Projective Schemes, continued
- 347 Altgeld Hall, 3:00 p.m.
- GALOIS MODULES
- Marcin Mazur, Department of Mathematics, UIUC
- The lifted root number conjecture, continued
- 245 Altgeld Hall, 4:00 p.m.
- MATHEMATICS COLLOQUIUM
- Albert Baernstein, Professor of Mathematics, Washington University, St. Louis
- The Stretch Conjecture for Lipschitz Functions In Rn
- Abstract: In this talk I will discuss a conjectural calculus inequality involving directional derivatives and Jacobian determinants of Lipschitz maps in Rn. The conjecture is suggested by Burkholder's
work on sharp inequalities for martingales and has ties to unsolved problems
in calculus of variations (rank one functions vs. quasiconvex functions),
harmonic analysis (norms of singular operators), quasiconformal
analysis (sharp distortion inequalities for quasiregular mappings in
Rn) and geometry (it proposes an almost-generalization of the
isoperimetric inequality).
- Refreshments at 3:15 p.m. in Room 321 Altgeld Hall
FRIDAY, APRIL 6
- 2 Illini Hall, 11:00 a.m.
- PROBABILITY AND STATISTICS SEMINAR
- Professor Zhiliang Ying, Department of Statistics, Columbia University
- Semiparametric analysis of transformation models
- Abstract: I will describe in this talk a new method for estimation of
regression parameters in semiparametric regression models, which
include the proportional hazards model and the proportional odds model
as special cases. It handles the usual right censorship in a natural
way. The estimate reduces to that of the maximum partial likelihood in
the case of the proportional hazards model. I will also present some
limited numerical results.
This is joint work with Kani Chen and Zhezhen Jin.
- 243 Altgeld Hall, 4:00 p.m.
- MODEL THEORY SEMINAR
- Professor Anand Pillay, Department of Mathematics, UIUC
- Zariski Geometries and Applications
- 314 Altgeld Hall, 3:00 p.m.
- MATHEMATICS IN SCIENCE AND SOCIETY
- Professor John Lawrence, University of Waterloo
- Group Theory and the Enigma
- Abstract: Professor Lawrence will describe his mathematical analysis
of the Enigma machine. In the early 1930s a young mathematician,
Marian Rejewski, led the Polish cipher bureau's attack on the German
military Enigma code machine. His work allowed the Polish cipher
bureau to read secret German communications until just before the
Second World War. Professor Lawrence will bring a working World War II
Enigma machine for demonstration.
This lecture, co-sponsored by CSL and MSS/Department of Mathematics,
is part of CSL's Golden Anniversary Spring Lecture Series.
- 314 Altgeld hall, 4:15 p.m.
- MATHEMATICS IN SCIENCE AND SOCIETY
- Dr. Simon Singh, author and broadcaster
- The Secret History of Public-Key Cryptography
- Abstract: Dr. Simon Singh, author of Fermat's Enigma, The Code Book,
and The Science of Secrecy, will lecture about the invention of public
key cryptography, an incredible encryption system that revolutionized
security and allowed the information age to blossom. He will reveal
the true story behind its invention, which was until very recently
hushed up by the British Government.
Dr. Singh is an author, journalist, and television producer
specializing in science and mathematics. Dr. Singh completed a
Ph.D. in particle physics at Cambridge University and at CERN in
Geneva. In 1990, he joined BBC's Science Department as a producer and
director of programs. In 1996, he directed Fermat's Last Theorem, a
documentary about the world's most notorious mathematical
problem. Most recently he directed a 5-part series called The Science
of Secrecy and wrote the companion book. www.simonsingh.com
This lecture, co-sponsored by CSL and MSS/Department of Mathematics,
is part of CSL's Golden Anniversary Spring Lecture Series.
- There will be a book signing and reception from 5:45-6:45 p.m. at the Author's Corner, Illini Union Bookstore
