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WEEKLY CALENDAR |
| Monday 7 |
3:10 pm, room 1431. Graph Theory and Combinatorics Seminar. Martin Kochol, Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia. Snarks with polyhedral embeddings in orientable surfaces. By a classical result of Tait, the four color theorem is equivalent with the statement that each 2-edge-connected 3-regular planar graph has a 3-edge-coloring. An embedding of a graph in a surface is called polyhedral if its dual has no multiple edges and loops. A conjecture of Grunbaum, presented in 1968, states that each 3-regular graph with a polyhedral embedding in an orientable surface has a 3-edge-coloring. With respect to the result of Tait, it aims to generalize the four color theorem for any orientable surface. We present a negative solution of this conjecture, showing that for each orientable surface of genus at least 5, there exists a 3-regular non 3-edge-colorable graph with a polyhedral embedding in the surface.
4:10-5:30 pm, room 1432. Subfactor Seminar. Romain Tessera, Vanderbilt University. Haagerup property and Poincare inequalities. We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincare inequalities, which can be formulated in terms of (generalized) expanders. We also give quantitative statements, relative to the compression. In the equivariant context, our result says that a group does not have the Haagerup property if and only if it has relative property T with respect to a family of probabilities whose supports go to infinity. We give versions of this result both in terms of unitary representations, and in terms of affine isometric actions on Hilbert spaces. See arXiv:0802.2541. |
| Tuesday 8 |
4:10-5:00 pm, room 1310.
Computational
Analysis Seminar. Razvan Teodorescu, Los Alamos National Laboratory. Planar harmonic growth with orthogonal polynomials. This talk will cover recent connections between the
theory of orthogonal polynomials with deformed
Bargmann kernel and harmonic growth of bounded
domains. Singular limits and refined asymptotics
will also be discussed.
4:10-5:15 pm, room 1431. Noncommutative Geometry Seminar. Piotr Nowak, Vanderbilt University. Isoperimetry of group actions. The notion of isoperimetric profiles is a generalization of isoperimetric dimension, which is a large-scale invariant. In the context of discrete groups isoperimetric profiles were introduced by Vershik, but were well-defined only for amenable groups. The purpose of this talk is a definition of an isoperimetric profile of an action of a finitely generated group on a compact Hausdorff space. We show that these profiles share many properties with original invariants for amenable groups/regularly exhaustible open manifolds. We also define the generalized isoperimetric profile of an amenable group via the action of G on its Stone-Cech compactification. For this last profile we explore the relation to growth and asymptotic dimension. We also compute the isoperimetric profile for several classes of groups for which the classical profile was not defined, e.g. hyperbolic groups. 4:10-5:30 pm, room 1432. Universal Algebra and Logic Seminar. Rostislav Horcik, Czech Republic Academy of Sciences, Prague: Applications of non-formally-integral totally ordered monoids in non-classical logics. Peter Cintula, Czech Republic Academy of Sciences, Prague: Hierarchies of implications and disjunctions in non-classical logics. --> 7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Justin Fitzpatrick, Vanderbilt University. Calculus by (counter)Example. The processes of computing limits, derivatives, and integrals, first seen in calculus, give us some very unusual constructions. In this talk, we'll see a figure with finite volume but infinite surface area, two seemingly equal expressions with different values, and many other peculiarities that give insight into the unusual nature of the infinitely large and the infinitely small. Free pizza. |
| Wednesday 9 | 4:10 pm, room 1310. Topology & Group Theory Seminar. Dave Witte Morris, University of Lethbridge (Canada). Some arithmetic groups that cannot act on the line. It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups (of higher real rank) also cannot act on the line. This problem remains open, but joint work with Lucy Lifschitz verifies the conjecture for many examples. This includes all finite-index subgroups of SL(2,Z[c]), where c is any irrational, real algebraic integer. The proof is based on the fact, proved by D.Carter, G.Keller, and E.Paige, that every element of these groups is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed. Note: This is a two-hour talk with a break after the first hour allowing people with other commitments to leave. |
| Thursday 10 |
3 pm, Preston Research Building 206. Special seminar co-sponsored by the Vanderbilt Integrative Cancer Biology Center and Emmanuele DiBenedetto. Dr. Vittorio Cristini, University of Texas, Austin. Computational modeling identifies morphological predictors of tumor invasion. Mathematical modeling based on first principles quantifies tumor growth's dependence on interactions between a set of variables - including genomic instability producing variations in sub-tumor clonal expansion and generating nutrient diffusion gradients - and demonstates that these determinants of heterogeneity, and not angiogenesis per se, conspire to produce the typical morphologic patterns of infiltrative tumor boundaries in histopathology. We demonstrate that heterogeneity in sub-tumor clonal expansion and nutrient consumption drives migration and proliferation of the emerging more aggressive clones up a nutrient concentration gradient within and beyond the central tumor mass. This heterogeneity and loss of cell adhesion trigger a gross morphologic instability that leads to replacement of less aggressive clones and separation of tumor cell strands or clusters infiltrating into adjacent tissue. This model allows all variables that characterize the biophysics of tumor growth to be considered and could be applied to determine the probabilistic behavior of tumors given their pathologic appearance.
4:10-5 pm, room 5211. Colloquium. Sergei Ivanov, University of Illinois at Urbana-Champaign. On Dehn functions of infinite presentations of groups. We discuss two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and indicate the fundamental equivalence between the solvability of the word problem for a group presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced functions (this equivalence fails for the standard Dehn function). Elaborating on this equivalence and making use of this function, we present a characterization of finitely generated groups for which the word problem can be solved in nondeterministic polynomial time. We also give upper bounds for these functions, as well as for the standard Dehn function, in the case of the Grigorchuk 2-group of intermediate growth and free Burnside groups of sufficiently large exponents, defined by some minimal systems of defining words. This talk is based on joint with R.I. Grigorchuk work. Tea at 3:30 pm in SC 1425. |
| Friday 11 |
3 pm, room 1320. Retirement celebration in honor of Profs. Matt Gould and Mike Plummer.
4:10-5 pm, room 1310. NCGOA Research Training Group Seminar. Bogdan Nica, Vanderbilt University. Stable Ranks. |