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| Monday 13 |
3:10-4 pm, room 1432. Graph Theory and Combinatorics Seminar. Petar Markovic, University of Novi Sad, Serbia. A survey of graph-theoretic Constraint Satisfaction Problem. In this talk I will give an overview of some of the major results concerning the following complexity theory question: For a finite directed
graph G, CSP(G) is the class of all finite directed graphs which may be
mapped homomorphically into G. The question is what is the complexity of
the membership problem of CSP(G), i. e. how hard is it to determine if a
finite directed graph H can be mapped into the fixed finite directed graph
G (the time-complexity is a function of the size of H, of course). The
conjecture, a special case of the fixed-template CSP Dichotomy Conjecture
by Feder and Vardi states that the only two complexities this problem may
have are P and NP-complete. I will give an overview of the result on this topic, belonging to four
major strains: 1) Feder and Vardi's proof that the general version of the fixed-template
CSP Dichotomy Conjecture is equivalent to its special case for graphs. 2) Nesetril and coauthors' series of results characterizing the first-order definable CSP graphs via finite duality. 3) Nesetril, Siggers and Zadori's proof of an equivalent condition to the
algebraic one for the desired NP-complete case of the general conjecture,
which in a sense 'graph finds 3-colorability' in any known NP-complete
case of the general problem. 4) A series of results of graphs with no sources and sinks, culminating in
the proof of the dichotomy conjecture in this case by Barto, Kozik and
Niven.
4:10-5 pm, room 1431. NCGOA Research Training Group Seminar. Bogdan Nica, Vanderbilt University. Elementary generation of the special linear group. |
| Tuesday 14 |
3:20 pm, room 1425. Graduate Student Tea.
4:10-5 pm, room 1432. Noncommutative Geometry Seminar. Guoliang Yu, Vanderbilt University. An equivariant index theorem and its applications. I will discuss an equivariant index theorem for the Dirac operator on noncompact manifolds and its applications to geometry and topology of three dimensional manifolds. This is joint work with Stanley Chang and Shmeul Weinberger. The talk should be accessible to general audience including graduate students. 4:10-5:00 pm, room 1312. Computational Analysis Seminar. Akram Aldroubi, Vanderbilt University. Compressive Sampling via Huffman codes. Let $x$ be some vector in $\R^n$ with at most $k$ much less than $n$ nonzero components (i.e., $x$ is a sparse vector). We wish to determine $x$ from inner products $\{y_i=a_i\dot x\}_{i=1}^m$, the samples. How can we determine a set of $m$ vectors $\{a_i\}$ such that $x$ can be completely determined from the samples $\{y_i=a_i\dot x\}_{i=1}^m$ by a computationally efficient, stable algorithm. The recent theory of compressed sampling addresses this problem using two main approaches: the geometric approach and the combinatorial approach. In this talk I will present a new information theoretic approach and use results from the theory of Huffman codes to construct a sequence of binary sampling vectors to determine a sparse vector $x$. Unlike the standard approaches, this new method is sequential and adaptive in the sense that each sampling vector depends on the previous sample value. The number of measurements we need is no more than $O(k\log n)$ and the reconstruction is $O(k)$ which is better than any other method. 4:30-5:30 pm, room 1308. Universal Algebra and Logic Seminar. Constantine Tsinakis, Vanderbilt University. Universal Algebra for the Working Mathematician. The title of the talk captures its aims. My intention is to provide an account of those fundamental results in the area that every well-educated research mathematician would find useful in his/ her research. One of the aims of universal algebra is to study features common to many familiar algebraic systems, such as groups, rings, lattices, etc. Such a study places a number of algebraic notions in their proper setting, reveals connections of seemingly unrelated concepts, and uses the higher level of abstraction to apply these results to entirely new situations. A central theme in this area is that of a variety or an equational class. 7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Alan Wiggins, Vanderbilt University. Magic Computers. In the 1980's, Richard Feynman suggested building a computer based on quantum mechanical principles. What does that mean? What would such a machine look like? Are they out there right now? We'll discuss these questions and what the theoretical limits on such machines would be. In particular, you CAN'T win a million dollars from the Clay Institute for making a "practical" quantum computer (unless you believe in traveling faster than the speed of light), but you CAN crack a host of security codes, which would get you even more from Microsoft. Free pizza. |
| Wednesday 15 | 4:10 pm, room 1310. Topology & Group Theory Seminar. Qayum Khan, Vanderbilt University. The Nil-Nil theorem in algebraic K-theory. Bass defined an exotic Nil-summand of the algebraic K-theory of a polynomial extension. Later, Waldhausen extended the definition to tensor algebras and defined an exotic Nil-summand of the algebraic K-theory of an injective amalgam of groups. The Nil-Nil theorem states, under a certain finiteness condition, that there is a natural isomorphism from the amalgam Nil to a tensor Nil. An important application is that the Farrell-Jones conjecture in algebraic K-theory can be sharpened from the family of virtually cyclic subgroups to the family of finite-by-cyclic subgroups of a discrete group G. This is joint work with J.F. Davis and A.A. Ranicki. Time permitting, we may discuss current work on the L-theoretic version, generalizing the UNil-NL theorem of Connolly--Ranicki. |
| Thursday 16 | 4:10-5 pm, room 5211. Colloquium. Steve Shkoller, University of California, Davis. On the analysis of Euler's equations of fluid dynamics with moving boundaries. Euler formulated a complete set of equations for the motion of fluids by 1755, and afterwards stated "...it is not the principles of Mechanics which we lack in the pursuit of these researches, but solely Analysis, which is not yet sufficiently cultivated for this purpose." The past 250 years has seen the development of this Analysis. In this lecture, I will describe some of the major mathematical developments, culminating with recent advances in the understanding of free-boundary and moving interface problems. The latter class spans the classical water-wave problem and the expansion of a gaseous star. Tea at 3:30 pm in SC 1425. |
| Friday 17 |
4:10-5:30 pm, room 1310.
Subfactor Seminar. Junhao Shen, University of New Hampshire. Topological Free Entropy Dimension for Blackadar and Kirchberg's MF algebras. We will start the talk with introduction to MF C*-algebras in the sense of Blackadar and Kirchberg. Then we will indicate the connection between MF C*-algebras and Brown-Douglas-Fillmore's extension semigroup. Basing on the work by Haagerup and Thorbjornsen on the reduced group C*-algebras of free groups, we will give several new examples of Blackadar and Kirchberg's MF algebras, followed by several new examples of C*-algebras whose BDF-extension semigroup is not group. In the second half of the lecture, we will introduce Voiculescu's topological free entropy theory for unital C*-algebras. We will see the reason why the definition of Voiculescu's free entropy is based on the properties of MF C*-algebras. Then we will present some calculation of topological free entropy dimension for several important classes of MF C*-algebras.
4:10 pm, room 1307. Partial Differential Equations Seminar. Pasquale Candito, Mediterranea University of Reggio Calabria, Italy. Critical point theory and its applications. The aim of the talk is to give some recent critical point results for nondifferentiable functionals and its applications to elliptic partial differential equations with discontinuous nonlinearities as well as to discrete boundary value problems. |
| Saturday 18 | Shanks Workshop: Dynamics of interfaces and structures in fluid flows. October 18-19. Organizers: Emmanuele DiBenedetto, Vanderbilt University, Mikhail Perepelitsa, Vanderbilt University, Gieri Simonett, Vanderbilt University. See http://sitemason.vanderbilt.edu/site/btCHS0/events. |
| Sunday 19 | Shanks Workshop: Dynamics of interfaces and structures in fluid flows. October 18-19. Organizers: Emmanuele DiBenedetto, Vanderbilt University, Mikhail Perepelitsa, Vanderbilt University, Gieri Simonett, Vanderbilt University. See http://sitemason.vanderbilt.edu/site/btCHS0/events. |