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Topic: Talk:Euler characteristic

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Euler characteristic Here's the abstract of my talk: Euler Characteristic versus Homotopy Cardinality Just as the Euler characteristic of a space is the alternating sum of the dimensions of its rational cohomology groups, the homotopy cardinality of a space is the alternating product of the cardinalities of its homotopy groups. In algebraic topology we learn that the Euler characteristic of a space is the alternating sum of the "ranks of the its rational homology groups", and we learn how to compute these using any way of chopping up the space into convex polytopes (or "cells"). The Euler characteristic is really a generalization of cardinality that allows negative numbers as values, so this other stuff is a further generalization that allows non-integral cardinalities. www.lns.cornell.edu /spr/2003-07/msg0052809.html   (623 words)

IMF: IMF Event Calendar The general version of the RR theorem for D-modules due to Schapira and Schneiders expresses the Euler characteristic of an elliptic D-module by the integral of its characteristic class, the so called microeuler class. Identification of microeuler class with the Connes-Karoubi chern class in negative cyclic homology 2. The purpose of this talk is to sketch the proof of the topological formula for this class (conjectured by Schapira and Schneiders). www.imf.au.dk /cgi-bin/dlf/viewevents.cgi?id=997&dlang=en   (116 words)

Seminars in Pure Mathematics Geometry & Topology Seminar In this talk we will describe several constructions of symplectic 4-manifolds with small Euler characteristic and positive signature, providing new examples of manifolds with exotic smooth structures. It is less clear whether such exotic structures exist when the Euler characteristic of the 4-manifold is small or the signature $\sigma$ of $H^2$ is positive. There are known many examples of simply connected 4-manifolds admitting infinitely many distinct smooth structures. www.math.uwaterloo.ca /PM_Dept/Research/Seminars/geom_top.shtml   (116 words)

USF Mathematics -- Colloquia, Spring 2005 In this talk, we introduce an analogous homology theory for graphs, whose graded Euler characteristic is the chromatic polynomial. In 1999, M. Khovanov introduced a graded homology theory for knots, and proved their graded Euler characteristic is the Jones polynomial. Invariance of domain refers to the property that the image of a relatively open set in a mapping's domain is an open set in the range space. www.math.usf.edu /Research/spring05/colloquia   (1491 words)

speakers.html This inspired us to defined two Samuel multiplicities, namely the shift and backward shift multiplicity, for a Fredholm operator to calculate the "Hilbertian Euler characteristic", that is, the Fredholm index. In the talk it is indicated that the smoothness issues for wavelets depend on a certain non-selfadjoint operator, one which first occurred in problems of statistical mechanics, having to do with phase transition, i.e., the coexistence of pure states, so called equilibrium states. This talk reports on work in progress which is joint with Gadadhar Misra. www.math.tamu.edu /research/workshops/linanalysis/speakers.html   (1491 words)

Program The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with A. This is joint work with Alicia Dickenstein (U. of Buenos Aires) and Bernd Sturmfels (U. Berkeley). In the second part of the talk, I will describe recent work with Stefan Papadima, in which we extend this "Rescaling Formula" for (rational) homotopy groups, to an arbitrary space with Koszul cohomology ring, and its corresponding sequence of homological rescalings. In this talk we introduce the contact-order filtration of the derivation module D(A) along the corresponding Coxeter arrangement A and prove that the filtration is essentially equivalent to the above-mentioned differential-geometric structures. www.math.lsu.edu /~cbms/program.html   (1491 words)

Algebraic Geometry Seminar: Autumn 2004 This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the complexified complement. In this talk, I will first introduce the notion of maximum likelihood degree of a statistical model. In this talk, we'll investigate the interplay between properties of the polytope and properties of the embedded variety (defining equations, free resolution, etc.). www.math.tamu.edu /~frank.sottile/seminars/AGS.html   (1491 words)

Junior Geometry: abstracts Hirzebruch's generalisation is harder to understand: he expresses the holomorphic Euler characteristic of a vector bundle E on a complex manifold M as a polynomial in the Chern classes of E and of M. The aim of this talk is to bridge the gap by looking at the case of complex surfaces. Roughly speaking, Grothendieck's idea (outlined in his lectures at IHES in 1966) was to lift varieties to characteristic zero and then take the de Rham cohomology to obtain "nice" (p-adic) cohomology. The original Riemann–Roch theorem determined, for generic divisors D on a compact Riemann surface R, the dimension of the vector space of meromorphic functions on R with poles "at worst D". www.ma.ic.ac.uk /juniorgeometry/abstracts.html   (6629 words)

UW-Madison Math Club He also calculated the indices of SL(2,Z/pZ) in SL(2,Z) as well as the Euler characteristic for SL(2,Z). Why We Like SL(2,Z) Alejandro Adem gave a rather in-depth talk about the group SL(2,Z) and its geometric interpretation. Now, if anyone asks you what you study or would like to know a little more about math, you can regale them with these stories instead of waxing lyrical about the joys of group theory. www.math.wisc.edu /~mathclub   (6629 words)

Junior Geometry: abstracts Hirzebruch's generalisation is harder to understand: he expresses the holomorphic Euler characteristic of a vector bundle E on a complex manifold M as a polynomial in the Chern classes of E and of M. The aim of this talk is to bridge the gap by looking at the case of complex surfaces. So a Kähler toric manifold is a Kähler manifold M equipped with the Hamiltonian action of T^m, and its polytope P is the image of M under the moment map (which coincides with a Legendre transformation). We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. www.ma.ic.ac.uk /juniorgeometry/abstracts.html   (6629 words)

The OSU Computer Science and Engineering Department The classic bounds on the sum of the Betti numbers, and their alternating sum (the Euler characteristic) are extended and improved in a variety of ways. Refreshments will be served immediately preceding the talk. Abstract: We present a survey of old and recent results on Betti number bounds and their applications to discrete and computational geometry. www.cse.ohio-state.edu /current-events/Speakers/AU04_Distinguished_Pollack.htm   (155 words)

Talk 2963 data/Spring_1999/0125 Consequently, one would like to compute the basic invariants (e.g., signature, Euler characteristic, fundamental group) of a smooth 4-manifold using the global monodromy of a given Lefschetz fibration on that 4-manifold. In particular he showed that every symplectic 4-manifold admits a smooth Lefschetz pencil, which can be blown up to yield a Lefschetz fibration over S^2. Conversely, Gompf showed that every smooth 4-manifold which admits a Lefschetz fibration (with a few exceptions) is in fact symplectic. www.math.duke.edu /mcal?abstract-2963   (119 words)

Junior Geometry: abstracts Hirzebruch's generalisation is harder to understand: he expresses the holomorphic Euler characteristic of a vector bundle E on a complex manifold M as a polynomial in the Chern classes of E and of M. The aim of this talk is to bridge the gap by looking at the case of complex surfaces. This invariant is sometimes—I expect always—equal to the Seiberg–Witten invariant of the underlying four-manifold. Operads are a formalization of the notion of algebraic structure. www.ma.ic.ac.uk /juniorgeometry/abstracts.html   (119 words)

TQFT Club Meeting 25-Nov-1999 In this talk I will try to describe, very briefly, the Atiyah's and Quinn's definitions of a TQFT and give an example of a class of TQFT's based on the Euler characteristic. One of the most important properties of a TQFT is the gluing axiom. I will try to show a new way of gluing spaces and the possibility of incorporating these ideas in a categorical language. www.math.ist.utl.pt /~rpicken/tqft/25_11_99.html   (119 words)

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