| Department of Mathematics and Statistics: 2007-08 Colloquia Oakland University |
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* Thursdays: Room 372 of the Science and Engineering Building (SEB 372), unless otherwise noted.
* Time: 3:00-4:00
* They are suceded by a 30 minutes refreshment period in SEB 368. Everyone is welcome.
* The URL www.oakland.edu/map is a map of Oakland University. Look for the SEB indication.
* Title, abstract and biographical information are added as they are provided by the speakers..
* Time: 3:00-4:00
* They are suceded by a 30 minutes refreshment period in SEB 368. Everyone is welcome.
* The URL www.oakland.edu/map is a map of Oakland University. Look for the SEB indication.
* Title, abstract and biographical information are added as they are provided by the speakers..
Abstracts:
Y. Kopeliovich: We apply Thomae formula and representation theory of Symmetric groups to derive relation between
theta functions evaluated at points of order 6 of the Jacobian of non singular cyclic covers of order 3 of the Sphere.
S. Wijesiri: Thomae’s formula expresses branch points of hyperelliptic curves in terms of the zero values of Riemann’s theta
functions with half integer characteristics. There have been attempts in the last two decade to generalize this result to larger
classes of algebraic curves. We will discuss some of these generalizations and describe explicit computations for normal cyclic
algebraic curves of small genus.
J. Gutierrez: Our world is not linear. Many phenomena, however, are often "linearized" because only then a reasonably well-
working mathematical machinery can describe the phenomena and produce meaningful forecasts.
Lattices are geometric objects that have been used to solve many problems in mathematics and computer science. Lattice
reduction strategies or the so called LLL-techniques seem inherently linear. The general idea of this technique is to translate
our non linear problem to finding a short vector in a lattice built from the nonlinear equation. Then, the so-called Shortest
Vector Problem and Closest Vector Problem in lattices play a major role. In recent years, these techniques have been used
repeatedly in algorithmic, coding theory and cryptography. In this talk, I will investigate lattice reduction technique on some
algebraic algorithms and cryptography problems, namely
- finding roots of multivariate integer polynomials and attacking cryptosystems,
- Integer factoring and RSA,
- computing subfields,
- predicting pseudorandom number congruential generators over Elliptic Curves,
- Cayley graphs: Groebner basis and LLL-reduced basis.
T. Shaska: We will give a brief review of algebraic curves and their automorphism groups. Furthermore, we will discuss
techniques of determining the automorphism groups of curves over fields of positive characteristic and determining the
equation of curves with a given automorphism group. Applications of algebraic curves in coding theory and cryptography will be
discussed if time permits.
D. Drignei: Applications in fields ranging from weather and climate, to biology and industry, increasingly use computer
experiments as substitutes for physical experiments in cases where the latter are difficult or impossible to perform. A
computer experiment consists of several runs of a computer model (or code) for the purpose of better understanding the
impact of various input conditions on the outcome of the experiment. One practical difficulty in computer experiments
is that computer model runs may require prohibitive amounts of computational resources. A recent approach uses statistical
approximations as computationally faster surrogates for such computer models. This talk presents computationally
efficient methodology to obtain such surrogates in cases where the computer output data are multidimensional.
H. Qu: High-throughput screening (HTS) is a large-scale process that screens hundreds of thousands to millions of compounds
in order to identify potentially leading candidates rapidly and accurately. There are many statistically challenging issues in HTS.
In this talk, I will focus the spatial effect in primary HTS. I will discuss the consequences of spatial effects in selecting leading
compounds and why the current experimental design fails to eliminate these spatial effects. A new class of designs will be
proposed for elimination of spatial effects. The new designs have the advantages such as all compounds are comparable within
each microplate in spite of the existence of spatial effects, the maximum number of compounds in each microplate is
achieved, etc. Optimal designs are recommended for HTS experiments with one control as well as multiple controls.
Y. Kopeliovich: We apply Thomae formula and representation theory of Symmetric groups to derive relation between
theta functions evaluated at points of order 6 of the Jacobian of non singular cyclic covers of order 3 of the Sphere.
S. Wijesiri: Thomae’s formula expresses branch points of hyperelliptic curves in terms of the zero values of Riemann’s theta
functions with half integer characteristics. There have been attempts in the last two decade to generalize this result to larger
classes of algebraic curves. We will discuss some of these generalizations and describe explicit computations for normal cyclic
algebraic curves of small genus.
J. Gutierrez: Our world is not linear. Many phenomena, however, are often "linearized" because only then a reasonably well-
working mathematical machinery can describe the phenomena and produce meaningful forecasts.
Lattices are geometric objects that have been used to solve many problems in mathematics and computer science. Lattice
reduction strategies or the so called LLL-techniques seem inherently linear. The general idea of this technique is to translate
our non linear problem to finding a short vector in a lattice built from the nonlinear equation. Then, the so-called Shortest
Vector Problem and Closest Vector Problem in lattices play a major role. In recent years, these techniques have been used
repeatedly in algorithmic, coding theory and cryptography. In this talk, I will investigate lattice reduction technique on some
algebraic algorithms and cryptography problems, namely
- finding roots of multivariate integer polynomials and attacking cryptosystems,
- Integer factoring and RSA,
- computing subfields,
- predicting pseudorandom number congruential generators over Elliptic Curves,
- Cayley graphs: Groebner basis and LLL-reduced basis.
T. Shaska: We will give a brief review of algebraic curves and their automorphism groups. Furthermore, we will discuss
techniques of determining the automorphism groups of curves over fields of positive characteristic and determining the
equation of curves with a given automorphism group. Applications of algebraic curves in coding theory and cryptography will be
discussed if time permits.
D. Drignei: Applications in fields ranging from weather and climate, to biology and industry, increasingly use computer
experiments as substitutes for physical experiments in cases where the latter are difficult or impossible to perform. A
computer experiment consists of several runs of a computer model (or code) for the purpose of better understanding the
impact of various input conditions on the outcome of the experiment. One practical difficulty in computer experiments
is that computer model runs may require prohibitive amounts of computational resources. A recent approach uses statistical
approximations as computationally faster surrogates for such computer models. This talk presents computationally
efficient methodology to obtain such surrogates in cases where the computer output data are multidimensional.
H. Qu: High-throughput screening (HTS) is a large-scale process that screens hundreds of thousands to millions of compounds
in order to identify potentially leading candidates rapidly and accurately. There are many statistically challenging issues in HTS.
In this talk, I will focus the spatial effect in primary HTS. I will discuss the consequences of spatial effects in selecting leading
compounds and why the current experimental design fails to eliminate these spatial effects. A new class of designs will be
proposed for elimination of spatial effects. The new designs have the advantages such as all compounds are comparable within
each microplate in spite of the existence of spatial effects, the maximum number of compounds in each microplate is
achieved, etc. Optimal designs are recommended for HTS experiments with one control as well as multiple controls.