Talks: **Combinatorics Seminar, UCLA, February 2, 2016.**
**Combinatorics Seminar, USC, February 1, 2016. Pattern occurrence in random permutations.**
**Combinatorics Seminar, UCSD, November 10, 2016.**
**Probability Seminar, UCSD, November 10, 2016.**
**Probability Seminar, UCLA, September 29, 2016. Poisson approximation of combinatorial assemblies with low rank.**
**Predictive Policing Workshop, ICERM, August 8 - 12, 2016. Presentation talk: A spacetime analysis of police calls for service in Providence, RI. (with Mahesh Agarval, David Lloyd, Monica Moreno, Naratip Santitissadeekorn, Talitha Washington)**
**Permutation Patterns 2016, Howard University, June 28, 2016. Pattern occurrence in random permutations.**
**(Workshop attended: Mathematical Problems in Industry Workshop, Duke University, June 13 - 17.)**
**Cultural Analytics, IPAM, June 9, 2016.****Mathematical methods in****Historical & Cultural Research:****the Case of****Soviet Children writers’****network representation. (with****Ekaterina Lapina-Kratasyuk)**
**GASCOM2016, Corsica, France, June 3, 2016. Improvements to exact Boltzmann samplers using probabilistic divide-and-conquer and the recursive method.**
**Frontier Probability Days, University of Utah, May 10, 2016. Exact sampling of combinatorial structures using probabilistic divide-and-conquer.**Slides
**Mathematical Physics and Probability, UC Davis, April 20, 2016. Limit shapes of restricted integer partitions under non-multiplicative conditions.**
**Algebra and Discrete Mathematics, UC Davis, April 18, 2016. Exact sampling of combinatorial structures.**
**Southern California Discrete Mathematics Symposium, UCLA, April 16, 2016. Exact sampling of combinatorial structures via probabilistic divide-and-conquer.**
We demonstrate a recent technique for exact sampling of combinatorial structures called probabilistic divide-and-conquer. By exploiting certain independence properties of the random variables which describe random component sizes, we are able to obtain efficient exact samplers, provably more efficient than exact Boltzmann samplers. The technique also generalizes to constrained structures with continuous-valued components. Applications include integer partitions, contingency tables, combinatorial polytopes. **Rutgers Experimental Mathematics Seminar, Rutgers University, March 24, 2016. Lower bound expansions for random Bernoulli matrices via novel integer partitions.**
We discussed a class of integer partitions which index the various ways in which a random Bernoulli matrix can be singular. Talk slides. Video Part 1. Video Part 2. **Cultural Analytics, IPAM, March 15, 2016. Your persistent back luck, and other notions from probability.**
I attempted to explain the birthday problem and Poisson approximation to a non-mathematical audience. At the end I showed how to estimate the probability of at least one person willing the lottery. Briefly, the big $1.3 billion dollar lottery sold about 635 million tickets, each with probability 1 / 292 million of winning. The expected number of winners is thus 2.17, and the number of winners is very closely Poisson distributed, thus there was about a 10% chance of no one winning the lottery, and pretty good chance that 1-3 people won it. I didn't have time to explain why you always pick the slow lane, and why your luck is always worse than your friends' luck. **Combinatorics Seminar, University of Southern California, February 24, 2016. On the number of integer partitions of size n: a quantitative analysis.**
This talk was for a graduate student audience, and described a number of subtleties involving asymptotic analysis related to the number of integer partitions. We also showed how using the analysis of Hardy, Ramnujan, Rademacher, and Lehmer, one can obtain auxiliary results like log-concavity. Talk Slides **Statistics Seminar, Rutgers University, February 12, 2016. Exact Sampling of Combinatorial Stochastic Processes**
A talk designed to explain the various aspects of probabilistic divide-and-conquer and how it can be applied in various scenarios. **San Jose State University, February 2, 2016. Poisson Approximation in Combinatorial Structures: Beyond the Birthday Problem**
An expository talk designed to showcase some applications of Poisson approximation in combinatorial structures. **Combinatorics Seminar, University of California, Los Angeles, January 28, 2016. Non-attacking rooks, Stirling numbers, and filling a gap with Poisson approximation.**
Based on the recent work with Richard Arratia accepted into the Annals of Combinatorics: Completely effective error bounds for Stirling Numbers of the first and second kind via Poisson Approximation **RIPS 2015 Special Seminar for undergraduate program participants, IPAM, UCLA, August 14, 2015. How to give a Spirited Talk! Full Video.**
Similar talk as the RIPS 2014 seminar. I volunteered to give a presentation on some of the techniques I use while teaching aimed at keeping the audience engaged. I also demonstrated ways in which I explain sometimes tedious and/or technical information. I showed them examples of my teaching style from recordings on BruinCast and then demonstrated several principles of good public speaking / performing. **Combinatorics Seminar, University of California, Los Angeles, March 12, 2015. Limit shapes of restricted integer partitions under non—multiplicative conditions**
Same talk as below, i.e., recent work with Igor Pak on limit shapes of restricted integer partitions. **Probability Seminar, University of California, Irvine, February 24, 2015.****Limit shapes of restricted integer partitions under non—multiplicative conditions**
Same talk as below, i.e., recent work with Igor Pak on limit shapes of restricted integer partitions. **Probability and Statistics Seminar, USC, December 5, 2014. Limit Shapes of Integer Partitions under non--Multiplicative conditions**
I gave a talk on some recent work with Igor Pak on limit shapes of restricted integer partitions. **RIPS 2014 Special Seminar for undergraduate program participants, IPAM, UCLA, August 13, 2014. Some tips on giving a talk.**
**Combinatorial Stochastic Processes, A conference in celebration of Jim Pitman's Work, UC San Diego, June 20-21, 2014.***Poisson approximation and Stein's method for the asymptotic enumeration of combinatorial sequences.*
I discussed recent work with Richard Arratia on how to use Poisson approximation in order to estimate combinatorial sequences. **Panelist at the CET Center for Excellence in Teaching, "teaching your first class." USC, April 21, 2014.**
I volunteered to be a panelist so that graduate students could ask questions about lecturing a class. **Probability and Statistics Seminar, USC, March 7, 2014. Stirling numbers and Poisson Approximation**
The Stirling numbers of the second kind can be written as the number of ways placing k rooks on the lower triangular half of an n by n board such that none are attacking. The Stirling numbers of the first kind is similar, except rooks are only allowed to attack column-wise. When k^2 = O(n) the number of pairs of attacking rooks is approximately Poisson distributed, and we can apply the Chen-Stein method to obtain guaranteed error estimates for the probability that no two rooks are attacking. The tricky part is defining the right coupling in Chen-Stein. This extends the range of available hard error estimates originally obtained by Moser and Wyman. **Combinatorics Seminar, UCLA, January 23, 2014. Asymptotics of partition functions and their applications**
A survey talk intended for a general audience. We discussed some of the history of the asymptotic enumeration of partitions under various restrictions, notably the work of Wright, Erdos and Bateman (not Batman), Roth-Szekeres, and Romik. At the end we demonstrated a connection to limit shapes. **PSTAT Seminar, UCSB, February 13, 2013. Probabilistic Divide-and-Conquer: A new method for exact simulation**
This was a 50-minute seminar based on the paper with the same name as the title. **Probability Seminar, UCLA, December 5, 2012. Random Bernoulli matrices and novel integer partitions**
A 50-minute seminar emphasizing the more probabilistic aspects of the paper with Arratia on the probability that a random Bernoulli matrix is singular. **Combinatorics Seminar, UCLA, October 11, 2012. How to randomly sample integer partitions of a fixed size.**
A very applied talk about various algorithms to sample integer partitions, for example, enumeration, the recursive method (Nijenhuis and Wilf), Fristedt's conditioning, and finally probabilistic divide-and-conquer. It was shown how a probabilistic algorithm for generating partitions was greatly enhanced by thinking combinatorially. **Probability/Statistics Seminar, USC, December 2, 2011. Random Bernoulli matrices and novel integer partitions.**
A talk explaining the structure of novel integer partitions and their use in characterizing a possible asymptotic expansion for the singular probability of random Bernoulli matrices. **Mathematics Clinic, Harvey Mudd College, October 30 2006. Low energy earth to moon mission design using invariant manifolds of the planar circular restricted 3-body problem**
I talked about the research over the summer of 2006 as part of the IPAM RIPS program (part of a team of 4 undergraduate researchers). The project was sponsored by JPL (Jet Propulsion Laboratory) under the guidance of an industry mentor (Martin Lo) and a faculty mentor (Stefano Campagnola) and the purpose was to investigate low-energy trajectories from the earth to the moon. These trajectories take advantage of halo orbits that emerge from an analysis of the Lagrange points in the 3-body problem. Our team coupled two 3-body problems together to provide candidate trajectories that could be optimized over the 4-body system, which is significantly harder to analyze. |

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