Seminars archive

One of the most powerful tools for improving success rates in introductory computing courses is the incorporation of context -- a theme that pervades the computing lectures, assignments, and examples which relates the content to a concrete application domain. Contextualized computing education has even allowed us to be successful with challenging audiences, such as the non-technical major. In this talk, we review why Georgia Tech has chosen to teach serious computer science to every student on campus, and then discuss research findings from several schools on the benefits and costs of contextualized computing education.

For central simple algebras of even degree with orthogonal involutions, invariants modeled on the discriminant and Clifford algebra of quadratic forms were defined by Jacobson and Tits, and a relative cohomological invariant of degree 3 is defined by using the Rost invariant of Spin groups when the first two invariants vanish. Its properties and computation will be discussed in the particular case where the algebra has degree 8 and index 4, in relation with properties of 8-dimensional quadratic forms in $I^2$. (Joint work with Anne Qu\'eguiner-Mathieu).

TBA

Discrete groups come in all shapes and sizes. I'll show you some. Then I'll explain what I think a quasi-isometry is.

It's easy to describe the set of $n$-by-$n$ complex matrices whose $r$-th power is zero: each is conjugate to a Jordan canonical form matrix with all eigenvalues 0 and blocks of size at most $r$. In this talk I will discuss work done by the University of Georgia VIGRE Algebra Group on generalizations of this problem. We will consider an arbitrary simple algebraic group $G$ over an algebraically closed field, along with certain embeddings of its Lie algebra $g$ into $n$-by-$n$ matrices, and describe the set of elements of $g$ whose $r$-th power is zero, in terms of $G$-conjugacy classes. As a corollary, when the characteristic is $p$, we obtain a description of the ``restricted nullcone'' of $g$ (the case $r=p$). When $p$ is a ``good prime'' (not too small), this verifies, by much more elementary methods, a 2003 result of Carlson, Lin, Nakano, and Parshall. And when $p$ is ``bad'' (very small), our results are new. Support varieties are geometric objects associated to cohomology rings and representations. In the case of modular representations of Lie algebras, the supports are subvarieties of the restricted nullcone. In the last part of my talk, I'll briefly define support varieties for Lie algebras, and then discuss how our VIGRE Algebra Group identified explicitly the support varieties of induced modules in the bad prime setting. This extends the 2002 verification by Nakano, Parshall, and Vella of a 1987 conjecture of Jantzen for good primes.

Many groups have the property of having only finitely many conjugacy classes of finite subgroups. Examples include hyperbolic groups, CAT(0) groups, mapping class groups, and automorphism groups of free groups. Do subgroups of these groups inherit this property? The answer turns out to be no. I will describe how combinatorial Morse theory can be used to produce couterexamples. This is joint work with Noel Brady and Matt Clay.

Constraint Satisfaction Problems (CSP) are commonly found in practice and finding effective representation language and efficient constraint solving techniques are important research areas. A recent development is the integration of CSP (specifically SAT) solvers with relational database systems to enable CSPs to be modelled using SQL, and solved within the database system. A key challenge in this integration is to keep the SAT encoding of SQL constraints small. In this work, we describe a divide-and- conquer technique for reducing the encoding of cardinality constraints. We present a number of experiments to show the improvements on performance.

The problem of characterizing and detecting surprisingly recurrent sequence patterns such as substrings or motifs and related associations or rules is pursued ubiquitously in order to compress data, unveil structure, infer succinct descriptions, extract and classify features, etc. In Molecular Biology, some such patterns are variously implicated in facets of biological structure and function. Because of that, Pattern Discovery constitutes one of the most battered, flourishing and arguably useful applications of Computational Molecular Biology. The very notion of a pattern still embodies subtleties and ambiguities, as do related concepts such as class and structure. And the discovery, particularly on a massive scale, of surprising patterns and correlations thereof poses interesting methodological and algorithmic problems, some of which appear to be hardly surmountable. This talk proposes a brief account of algorithmic pattern discovery under constraints of saturation, displays some of its applications, and highlights issues, products and challenges emerged in recent and current work.

V.~Kac classified finite dimensional simple Lie superalgebras over the field of complex numbers in 1970s. They constitute several series and are divided into two types based on their even part: classical type and Cartan type. Lie superalgebras of Cartan type consists of four series $W(n)$, $S(n)$, $S^{~}(n)$, and $H(n)$. In this talk I will briefly introduce Cartan type Lie superalgebras and then I will show how explicitly one can compute cohomology and support varieties for $W(n)$ and $S(n)$. I will also mention what we have for $H(n)$ and present a new theorem on realizability of support varieties that holds both for classical and Cartan type Lie superalgebras. If I have time I am planning to present some open problems at the end of my talk. The results about $W(n)$ represents joint work with Jonathan Kujawa and Daniel Nakano.

Information-centric collaborative sites have emerged as viable sources for many information needs. In particular, the Community Question Answering (CQA) model has evolved as an effective alternative to web search: users post questions and answers, and rate and evaluate each other’s content. As a result, users contribute both content and rich interaction metadata in their roles as askers, answerers, and evaluators. To give a sense of the scale, just one popular site, Yahoo! Answers, has attracted an active participation of millions of users, and has amassed a searchable archive of hundreds of millions of answers to tens of millions of questions. The talk will build on our earlier work on modeling user interactions in web search, and will describe new problems related to mining this user-generated content, including estimating content quality, contributor authority, user intent, and asker satisfaction with the results.

We know, thanks to the work of A. Weil, that counting points of varieties over finite fields yields purely topological information about them. For example, an algebraic curve is topologically a certain number g of donuts glued together. The same number g, on the other hand, determines how the number of points it has over a finite field grows as the size of this field increases. This interaction between complex geometry, the continuous, and finite field geometry, the discrete, has been a very fruitful two-way street that allows the transfer of results from one context to the other. In this talk I will first describe how we may count the number of points over finite fields for certain character varieties,parameterizing representations of the fundamental group of a Riemann surface into GL-n. The calculation involves an array of techniques from combinatorics to the representation theory of finite groups of Lie type. I will then discuss the geometric implications of this computation and the conjectures it has led to. This is joint work with T. Hausel and E. Letellier

We know how search engines crawl websites: they harvest links from pages and iterate through each to develop an "image" of the world wide web as a whole. During the last decade of search engine growth, websites have attempted to "help" or even to more directly influence the crawlers and the subsequent website ranking. For example, conventional wisdom holds that search engines "prefer" sites that are wide rather than deep, and that having a site index will result in more thorough crawling by the Big Three crawlers: Google, Yahoo, and MSN. But how do crawlers actually behave on websites? Does site design really affect this behavior? We created a series of 10 websites to monitor search engine behavior when crawling with very large websites (wide and deep), as well as their behavior on websites where resources "disappear." We analyzed the logs of each of these sites for over a full year to see if the conventional wisdom holds true. GIF animations of Apache log data are used to illustrate the crawling patterns. We found that each search engine exhibited different behavior and crawl persistence, and that site design does appear to affect this behavior. We plot the progress of the crawlers through the sites, and their behaviors regarding the various file types. A side benefit of search engine activity on a site is the "cached page" which is accessible if the original is unavailable. How long will such pages persist in the cache if the web source page disappears? We examine this issue and the role that the cache and a website's design play in website preservation.