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University of Kentucky |
| Regular Faculty:
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Current Doctoral Students:
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Emeriti and Former Members:
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Former Doctoral Students:
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Seminar:
In Spring 2008 our seminar takes place Tuesdays, 3:00 - 4:00 pm, in POT 845.
Coordinator: Uwe Nagel
Schedule:
- Gorenstein Approximations, Dual Filtrations, and Applications , Tony Puthenpurakal (IIT Bombay),
April 29, 2008
- An Introduction to Low-Density Parity-Check Codes, Christine Kelley (Ohio State University), April 22, 2008
- Poincare Series for Diagonal Forms, Dibyajyoti Deb (UKY), April 8, 2008
- Building Public Key Crypto-Systems from Semi-Rings, Joachim Rosenthal (Zürich), April 3, 2008
- The Slice Algorithm, Bjarke Roune (Aarhus), April 1, 2008
- Simplicial Complexes and Algebraic Statistics, Erik Stokes (UKY), March 18, 2008
- Gorenstein Hilbert functions, Juan Migliore (Notre Dame), March 4, 2008
- Introduction to the Milnor Fibration, Darren Tapp (UKY), January 30, February 5, February 19, 2008
In Fall 2007 our seminar takes place Tuesdays, 3:30 - 4:30 pm, in POT 845.
Coordinator: Uwe Nagel
Schedule:
- Minimal Linkage, Uwe Nagel (UKY), November 27, 2007
- How to use the CD-index, Michael Slone (UKY), October 30, 2007
- Ordered Fields and Quadratic Forms, Claus Schubert (UKY), October 23, 2007
- An Open Problem on Hierarchical Models and Simplicial Complexes, Erik Stokes and Sonja Petrovic (UKY),
October 16, 2007
- Edge Ideals of Trees, Rachelle Bouchat (UKY), October 9, 2007
- Groebner Bases and List Decoding of BCH Codes, Philip Busse (UKY), October 2, 2007
- Algebraic properties of cut ideals, Sonja Petrocvic (UKY), September 25, 2007
- The arithmetic degree of squarefree strongly stable ideals, Eric Stokes (UKY), September 11, 2007
- Specializations of Ferrers ideals, Uwe Nagel (UKY), September 4, 2007
Previous seminars can be found here.
Graduate Courses in Algebra, Spring 2008:
- MA 661 - Modern Algebra II -
H. Gluesing-Luerssen
- MA 764 - Selected Topics in Algebra: Representation Theory - J. Beidleman
- MA 765 - Selected Topics in Algebra: Module Theory - E. Enochs
Graduate Courses in Algebra, Fall 2007:
- MA 561 - Modern Algebra I -
H. Gluesing-Luerssen
- MA 565 - Linear Algebra - E. Enochs
- MA 764 - Selected Topics in Algebra - J. Beidleman
Previous graduate courses (since 2001) can be found here.
Upcoming Events:
Former Events:
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Three Challenges of Claude Shannon,
Eighth Annual Hayden-Howard Lecture presented by Joachim Rosenthal, University of Zürich (Switzerland) , April 2, 2008.
This talk is suitable for advanced undergraduates!
Abstract: In 1948/1949 Claude Shannon wrote two papers [Sha48,Sha49] which
became the foundation of modern information theory. The papers
showed that information can be compressed up to the `entropy',
that data can be transmitted error free at a rate below the
capacity and that there exist provable secure cryptographic
systems. These were all fundamental theoretical result. The
challenge remained to build practical systems which came close to
the theoretical optimal systems predicted by Shannon.
In this overview talk we will explain how the first two
challenges concerning coding theory have resulted in practical
solutions which are very close to optimal. Then we explain why
the gap between the practical implementation of cryptographic
protocols with the theoretical result of Shannon is
largest.
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UIC-Purdue Workshop,
December 2-3, 2006.
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The History of Imaginary Numbers presented by
Robin Hartshorne,
University of California (Berkeley).
April 6, 2006.
This talk is suitable for all undergraduates!
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Midwest Algebra, Geometry and their Interactions Conference
(MAGIC 05),
October 7-11, 2005.
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Lipman-Fest,
May 17-21, 2004.
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Bluegrass Algebra Conference and Hayden-Howard Lectureship,
April 11-13, 2003.
Colloquia in Algebra and Geometry:
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The History of Imaginary Numbers,
Robin Hartshorne, University of California (Berkeley),
April 6, 2006.
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Algebraic Description and Effective Computation of Certain
Structures in Algebraic Geometry,
Aron Simis, Universidade Federal de Pernambuco (Brazil),
April 4, 2006.
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On the Core of Ideals,
Claudia Polini, University of Notre Dame, April 3, 2006.
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h-vectors of Gorenstein Polytopes,
Tim Römer, University of Osnabrück (Germany),
March 9, 2006.
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Design and Analysis of Convolutional Codes,
Heide Gluesing-Luerssen, University of Groningen (The Netherlands),
January 31, 2006.
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How to detect finiteness of Gorenstein homological dimension,
Lars Winther Christensen, University of Nebraska,
November 10, 2005.
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Rationality of the Zeta function of a finite graph,
Hyman Bass, University of Michigan,
September 23, 2005.
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Some expected properties of algebras,
Uwe Nagel, University of Kentucky,
November 14, 2002.
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Some things Ramanujan may have had up his sleeve,
George Andrews, Penn State,
March 4, 2002.
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Aspects of Liaison Theory,
Uwe Nagel, University of Paderborn (Germany),
February 15, 2002.
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Intersection multiplicities,
Anurag Singh, University of Utah,
February 4, 2002.
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Gorenstein Artin algebras,
Hema Srinivasan, University of Missouri,
November 20, 2001.
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Simultaneous resolutions,
Dale Cutkosky, University of Missouri,
November 19, 2001.
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Zero cycles, Euler class and existence of unimodular elements,
Shrikant M. Bhatwadekar, Tata Institute of Fundamental Research,
November 1, 2001.
Sample Qualifying Coursework for Doctoral Students:
MA 565 - Linear Algebra
| Vector spaces: |
Basic definitions, dimension, matrices and linear transformations.
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MA 561 - Modern Algebra I
| Groups: |
Basic definitions, isomorphism theorems, permutation groups,
structure of finitely generated abelian groups, groups acting on sets,
the Sylow theorems, solvable groups.
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| Rings: |
Basic definitions, ideals, prime and maximal ideals, quotient rings, Euclidean rings,
PID's and UFD's, field of fractions, polynomial rings, irreducibility criteria.
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MA 661 - Modern Algebra II
| Fields: |
Algebraic extensions, splitting fields, separable extensions, finite fields.
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| Galois Theory: |
Fundamental Theorem of Galois Theory, Galois group of polynomials,
solvability of polynomial equations, symmetric polynomials.
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Suggested text:
Abstract Algebra (3rd edition), by D. Dummit and R. Foote
Preliminaries; Ch. 1; Ch. 2; Ch. 3; Ch. 4; Ch. 6 (sect. 1);
Ch. 7; Ch. 8; Ch. 9; Ch. 13; Ch. 14
Additional texts:
Algebra, by T. Hungerford
Ch. 1 (sec. 2-6); Ch. 2 (sec. 1, 2, 4-8); Ch. 3;
Ch. 4 (sec. 1, 2, 6); Ch. 5 (sec. 1-6, 9); Ch. 8 (sec. 1-3)
Algebra (2nd edition), by S. Lang
Ch. 1 (sec. 1-6, 10); Ch. 2; Ch. 3 (sec. 1,2, 5); Ch. 5;
Ch. 6 (sec. 1-5); Ch. 7; Ch. 8 (sec. 1-3, 7); Ch. 15 (sec. 2)
Here are some old prelim exams:
Last modified: July 15, 2008
Page maintained by Heide Gluesing-Luerssen
