Class meetings: M 9-11 am, in KAP 245.

Office Hours: WF 10:15-11:45am.

Walk-ins and appointments at other time are welcome.

** The objective this semester: ** To discuss current research projects and future plans of participating students.

** Participating students: ** Emre Demirkaya, Michael Earnest, Enes Ozel, Haining Ren,
Melike Sirlanci, Weisheng Xie, Xiaojing Xing.

** What we did **

** Friday, January 16 (5-6pm):** organizational meeting

** Monday, January 19:** no meeting (MLK Day)

** Monday, January 26:** Michael's presentation about the longest common pattern in a random permutation.
Bottom line: longest increasing subsequence [which is the longest common pattern with the identity permutation] is of order n^{1/2},
longest common subsequence [when the size of the alphabet is fixed] is of
order n, but the longest common pattern of two randomly selected permutations [when the
pattern is not fixed a priori] is of order n^{2/3}.

A problem to think about.

** Monday, February 2:** Xiaojing's presentation about the
stochastic Perron method in the
linear case, with an eye toward the
non-linear case.

** Monday, February 9:** Emre's presentation about probabilistic methods in the study of matrix operators.

** Monday, February 16:** no meeting (Presidents' Day)

** Monday, February 23:** Enes's presentation about restricted permutations,
following a paper
by Persi Diaconis, Ronald Graham, and Susan P. Holmes.

** Monday, March 2:** Melike's presentation on numerical methods for SODEs following
a
paper from SIAM Reviews.

** Monday, March 9: ** Haining's presentation about signed permutations; lots of open problems.

** Monday, March 16: ** no meeting (spring break)

** Monday March 23: ** Weisheng's presentation on limit order books and high-frequency trading.
Limit order book is a list of prices and shares of stock people want to buy and sell. Knowledge of
the current limit order book makes it possible
to make money by trading fast, that is,
using high-frequency trading algorithm. The AC (Almgren-Chriss) model is one way to quantify the idea.

** Monday March 30: ** Guest lecture by Gene Kim on a special
type of permutations in S_{2n} (involutoins without fixed points, hence a product of n
transpositions; there are exactly (2n-1)!! of those).

** Monday, April 6:** Enes's presentation about Fibonacci permutations
(those consisting of transpositions and fixed points only),
covering limit theorems and several possible generalizations.

** Monday, April 13:** Haining's presentation in preparation for upcoming defense.

** Monday, April 20:** Michael's presentation on generating an arbitrary random number using
many tosses of a fair coin.

** Monday, April 27:** Melike's presentation on mean-square stability of various numerical
methods for SODEs.