Seminars in August 2015

  • 1st Korean Workshop on Graph Theory
    1st Korean Workshop on Graph Theory
    August 26-28, 2015
    KAIST  (E6-1 1501 & 3435)
    • Program Book
    • Currently, we are planning to have talks in KOREAN.
    • Students/postdocs may get the support for the accommodation. (Hotel Interciti)
    • Others may contact us if you wish to book a hotel at a pre-negotiated price. Please see the website.
    • We may or may not have contributed talks. If you want, please contact us.
    • PLEASE REGISTER UNTIL AUGUST 16.
    Location: KAIST
    • Room 1501 of E6-1 (August 26, 27)
    • Room 3435 of E6-1 (August 28)
    Invited Speakers:
    Organizers:
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  • Madhu Sudan, Reliable Meaningful Communication

    FYI: A seminar organized by Prof. Jinwoo Shin.

    Reliable Meaningful Communication
    Madhu Sudan Microsoft Research New England / MIT, Cambridge, MA, USA
    2015/08/06 Thu 3PM Room 102, Bldg. N1.
    Around 1940, engineers working on communication systems encountered a new challenge: How can one preserve the integrity of digital data, where minor errors in transmission can have catastrophic effects? The resulting theories of information (Shannon 1948) and error-correcting codes (Hamming 1950) created a “marriage made in heaven” between mathematics and its applications. On the one hand emerged a profound theory that could measure information and preserve it under a variety of errors; and on the other hand the practical consequences propelled telephony, satellite communication, digital hardware and the internet. In this talk I will give a brief introduction to the history of the mathematical theory of communication and then describe some of my work in this area that focus on efficient algorithms that can deal with large amounts of error, and on communication when sender and receiver are uncertain about each other’s context.</p>
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  • Jinfang Wang, Big Math Data: possibilities and challenges
    Big Math Data: possibilities and challenges
    Jinfang Wang
    Institute: Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Japan.
    2015/08/05 Wed 4PM-4:50PM
    The computer has influenced all kinds of sciences, with mathematical sciences being no exception. Mathematicians have been looking for a new foundation of mathematics replacing ZFC (Zermelo-Fraenkel set theory with the axiom of choice) and category theory, both of which have been successful to a great extent. Indeed, a theory, known as Type Theory, is rising up as a powerful alternative to all these traditional foundations. In type theory, any mathematical object is represented as a type.
    Various formal proof systems, including HOL, Isabelle, Idris, Coq, Agda, are based on this theory. Thanks to this new theory, it is becoming a reality that mathematical reasoning can indeed be digitized. Philosophers, logicians, computer scientists, and mathematicians as well, have been making a great deal of efforts and progresses to formalize various mathematical theories. Recent breakthroughs include, but not limited to, the computer-verified proofs of the Four Color Theorem (2004), the Feit Thomson Theorem (2012), and the Kepler Conjecture (2014).
    To formalize the proofs of these theorems, large amount of mathematical theories have been digitized and stored in the form of libraries (analogies of R libraries familiar to our statisticians). For instance, the formal proof of the Feit Thomson Theorem had involved 170,000 lines of codes with more than 15,000 definitions and 4,200 lemmas. These large data, referred to as Big Math Data hereafter, open a new paradigm and present serious challenges for statisticians to analyze a totally different type of data we have never experienced before, namely the mathematical theories. The right figure shows some libraries which form SSReflect, an extension of the interactive theorem prover Coq. There are many other libraries available as the results produced in the process of formalizations of various mathematical theories.
    In this talk, I shall give a gentle introduction to Big Math Data, and describe the possible mathematical and statistical challenges for both obtaining and analyzing Big Math Data.
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  • Yaokun Wu, Graph dynamical systems: Some combinatorial problems related to Markov chains
    Graph dynamical systems: Some combinatorial problems related to Markov chains
    Yaokun Wu
    Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China
    2015/8/5 Wed 3PM-3:50PM
    An order-t Markov chain is a discrete process where the outcome of each trial is linearly determined by the outcome of most recent t trials. The set of outcomes can be modelled by functions from a set V to a set F. The linear influences can be described as t-linear maps. When t=1, the set of linear influences can be conveniently described as digraphs on the vertex set V. Most of our talk is concerned with a combinatorial counterpart of Markov chains, where we can only tell the difference between zero probability and positive probability. We especially focus on the Boolean case, namely F is a 2-element set. This talk is to introduce several easy-to-state combinatorial problems about discrete dynamics, which arise from the combinatorial considerations of Markov chains.
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