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29 Geometry and Topology
Geometry and Topology Speaker: Thomas Huttemann (Belfast) "Algebraic K-theory of projective toric schemes" Time: 15:30 Room: MC 107 A projective toric scheme is specified by combinatorial data, viz., a
polytope with integral vertex coordinates. I will show how the geometry of
the polytope leads to a simple splitting result in the algebraic K-theory
of the scheme. In the special case of projective space (given by a standard
simplex) this reduces to the well-known splitting of K(P^n) into n+1 copies
of the K-theory of the ground ring. - The combinatorial approach is
flexible enough to include the case of schemes defined over an arbitrary
(possibly non-commutative) ring.
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30 Pizza Seminar
Pizza Seminar Speaker: Ali Moatadelro (Western) "Untying Knots with the Jones Polynomial" Time: 16:30 Room: MC 107 A knot is a smooth embedding of a circle in \(R^3\). A major problem in knot theory is to classify knots. Two knots are identified if one can transform one knot to the other one without tearing. The discovery of the Jones polynomial in 1980's has been considered as a great achievement in the classification of knots. The Jones polynomial is a sensitive knot invariant which is easy to compute. On the other hand, theories including geometry of low dimensional spaces, quantum groups and statistical mechanics meet each other because of this polynomial. In this talk we introduce the Jones polynomial in an elementary way from two different point of views. This talk will be accessible to undergraduate students. |
1 Operads Seminar
Operads Seminar Speaker: Marcy Robertson (Western) "Koszul Duality II" Time: 14:30 Room: MC 108 |
2 Colloquium
Colloquium Speaker: Pierre Guillot (Strasbourg) "A new link invariant" Time: 15:30 Room: MC 107 I am going to explain gently how one can define link invariants using braid groups and their representations as matrices. Then I am going to explain how representations endowed with a compatible symplectic form give rise to link invariants with values in the Witt ring of the field considered; of course I will define the Witt ring as well. The construction makes use of Maslov indices. In the end, using the Burau representation, we get one invariant which "contains" many others: signatures, Jones metaplectic nvariants, and a polynomial which is almost the one by Alexander-Conway.
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3 Algebra Seminar
Algebra Seminar Speaker: Pierre Guillot (Strasbourg/PIMS) "Lazy cohomology" Time: 14:30 Room: MC 107 There is a general cohomology defined by Sweedler for co-commutative Hopf algebras, generalizing the usual cohomology of a group or a Lie algebra. Recently it was discovered that low-dimensional groups could be defined without the co-commutativity requirement. In joint work with Christian Kassel, we have given the first few examples of computations with these, in the case of algebras of functions on groups. These turn out to be related to torsors in algebraic geometry, and Drinfeld twists in quantum groups theory. |
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9 Colloquium
Colloquium Speaker: Eric Jespers (Vrije Universiteit Brussel) "Groups, Group Rings and Set Theoretic Solutions of the Yang-Baxter Equation" Time: 15:30 Room: MC 107 In recent years there has been quite some
interest in the ``simplest'' solutions of the
Yang-Baxter equation. Such solutions are
involutive bijective mappings $r:X\times X
\rightarrow X\times X$, where $X$ is a finite
set, so that $r_{1}r_{2}r_{1}=r_{2}r_{1}r_{2}$,
with $r_{1}=r\times id_{X}$ and $r_{2}=id_{X}
\times r$. In case $r$ satisfies some
non-degeneracy condition, Gateva-Ivanova and Van
den Bergh, and also Etingof, Schedler and
Soloviev, gave a beautiful group (monoid)
theoretical interpretation of such solutions.
Such groups (monoids) are said to be of $I$-type.
In this lecture we give a survey of recent
results on the algebraic structure of these
groups (monoids) and their group (monoid)
algebras. |
10 Algebra Seminar
Algebra Seminar Speaker: Sheldon Joyner (Western) "Pullback of parabolic bundles and covers of the thrice-punctured sphere" Time: 14:30 Room: MC 107 A $G$-cover of a smooth projective curve $X$ over some algebraically closed field of characteristic zero ramified at a finite set $D$ of points, may be identified with a tensor functor from the category of finite representations of $G$ into bundles with parabolic structure along $D$, by work of Nori. Now when $X$ is the sphere and $D= \{0,1,\infty\},$ the parabolic bundle is of the form of $\oplus\mathcal{O}(s_i)$ for some integers $s_i$. These constants are very difficult to determine in general, but Ajneet Dhillon devised a clever method of bounding them using group theoretic data, and this is the subject of my talk. |
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Mathematics Calendar 
December 2010
