Welcome to the *Algebra and its Applications* seminar
home page!

The seminar is organized by Ettore Aldrovandi. Please send an email to contact me.

The seminar meets on Thursdays, 2:00-3:15pm in 104 LOV

January 15 | Organizational meeting |
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January 22 | No meeting (Departmental ext. review) |
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January 29 | Ettore Aldrovandi, FSU | Tame Symbols |
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After the break we resume our discussion of the *Tame
Symbol*. We will review what has been discussed in
the previous meetings and finish the Deligne
construction in terms of the Dilogarithm function.

The following is the general abstract for these talks:

TheFebruary 5 | No meeting (pre-empted by GPC meeting) |
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February 12 | Ettore Aldrovandi, FSU | Tame Symbols, II |
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We complete Deligne construction and prove some important properties of the Tame Symbol, hopefully including its holonomy characterization.

We also mention a few more applications: regulator maps
from *K*-theory, hermitian-holomorphic classes.

February 19 | Ettore Aldrovandi, FSU | Tame Symbols III |
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We sketch Bloch's construction of the global regulator map
from *K _{2}* to Deligne cohomology for a
complete curve

February 26 | Sam Huckaba, FSU | Integral closures of ideals, normality, and blowup algebras |
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March 4 | Sam Huckaba, FSU | Integral closures of ideals, normality, and blowup algebras II |

Integrality over an ideal plays an important role in commutative algebra and algebraic geometry (specifically, in the process of blowing up) as does the more commonly known concept of an integral ring extension. These talks will review the definitions and backgrounds of both, and will work towards descriptions of some recent research on the topics.

March 11 | Spring break |
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March 18 | Matilde Marcolli, MPI & FSU | Quantum Statistical Mechanics of Q-lattices |
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In this joint work with Alain Connes we generalize the
Bost-Connes dynamical system with arithmetic spontaneous
symmetry breaking to a system for **GL**_{2}
of adèles. The underlying noncommutative space is
the set of 2-dimensional **Q**-lattices up to scaling,
modulo commensurability.

March 25 | Sam Huckaba, FSU | Integral closures of ideals, normality, and blowup algebras III |
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April 1 | Sam Huckaba, FSU | Integral closures of ideals, normality, and blowup algebras IV |

April 8 | Sam Huckaba, FSU | Integral closures of ideals, normality, and blowup algebras V |

This is the second series (III, IV, and V) after the interruption

Integrality over an ideal plays an important role in commutative algebra and algebraic geometry (specifically, in the process of blowing up) as does the more commonly known concept of an integral ring extension. These talks will review the definitions and backgrounds of both, and will work towards descriptions of some recent research on the topics.

April 15 | Dimitre Tzigantchev, FSU | Linear orbits of line configurations |
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April 22 | Dimitre Tzigantchev, FSU | Linear orbits of line configurations II |

We study the action of the group of linear transformations on spaces of plane curves, and in particular on curves consisting of unions of lines. The main goal is the computation of a projective enumerative invariant in terms of the combinatorics of the line configuration.