Seminars and Colloquia by Series

On a conjecture of Graham on the p-divisibility of central binomial coefficients

Series
Combinatorics Seminar
Time
Friday, September 16, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Ernie CrootGeorgia Institute of Technology

I will discuss an old conjecture of Ron Graham on whether there are infinitely many integers $n$ so that $\mathrm{gcd}({{2n} \choose n}, 105)=1$, as well as recent progress on a version of this problem where 105 is replaced with a product of $r$ distinct primes. This is joint work with Hamed Mousavi and Maxie Schmidt.

Smooth structures on open 4-manifolds II

Series
Geometry Topology Working Seminar
Time
Friday, September 16, 2022 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John EtnyreGeorgia Tech

Please Note: One of the most interesting and surprising features of manifold topology is the existence of topological 4-manifold that admit infinitely many smooth structures. In these talks I will discuss what is known about these “exotic” smooth structures on open manifolds, starting with R^4 and then moving on to other open 4-manifolds. We will also go over various constructions and open questions about these manifolds.

When dynamics meet machine learning

Series
Time
Friday, September 16, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Online
Speaker
Molei TaoGeorgia Tech

https://gatech.zoom.us/j/95197085752?pwd=WmtJUVdvM1l6aUJBbHNJWTVKcVdmdz09

Abstract:  The interaction of machine learning and dynamics can lead to both new methodology for dynamics, and deepened understanding and/or efficacious algorithms for machine learning. This talk will give examples in both directions. Specifically, I will first discuss data-driven learning and prediction of mechanical dynamics, for which I will demonstrate one strong benefit of having physics hard-wired into deep learning models; more precisely, how to make symplectic predictions, and how that probably improves the accuracy of long-time predictions. Then I will discuss how dynamics can be used to better understand the implicit biases of large learning rates in the training of machine learning models. They could lead to quantitative escapes from local minima via chaos, which is an alternative mechanism to commonly known noisy escapes due to stochastic gradients. I will also report how large learning rates bias toward flatter minimizers, which arguably generalize better.

Polynomials over ordered blueprints and tracts

Series
Algebra Student Seminar
Time
Friday, September 16, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor GunnGeorgia Tech

I will introduce the concept of an ordered blueprint and a tract and discuss some algebraic and categorical properties. I will then discuss the notion of a "tropical extension" and discuss the theory of polynomials in these contexts.

Families of Lefschetz Fibrations via Cyclic Group Actions

Series
Geometry Topology Seminar
Time
Monday, September 12, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nur SaglamGeorgia Tech
Using various diagonal cyclic group actions on the product manifolds Σgg for g>0, we obtain some families of Lefschetz fibrations over S^2. Then, we study the monodromies of these families applying the resolution of cyclic quotient singularities. We also realize some patterns of singular fibers and study deformations of these Lefschetz fibrations. Some cases give rise to nice applications using rational blow-down operation. This is a joint work with A. Akhmedov and M. Bhupal.

 

Neural Oracle Search on N-BEST Hypotheses

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 12, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005 and https://gatech.zoom.us/j/98355006347
Speaker
Tongzhou ChenGoogle

In this talk, we propose a Neural Oracle Search(NOS) model in Automatic Speech Recognition(ASR) to select the most likely hypothesis using a sequence of acoustic representations and multiple hypotheses as input. The model provides a sequence level score for each audio-hypothesis pair that is obtained by integrating information from multiple sources, such as the input acoustic representations, N-best hypotheses, additional 1st-pass statistics, and unpaired textual information through an external language model. These scores are then used to map the search problem of identifying the most likely hypothesis to a sequence classification problem. The definition of the proposed model is broad enough to allow its use as an alternative to beam search in the 1st-pass or as a 2nd-pass, rescoring step. This model achieves up to 12% relative reductions in Word Error Rate (WER) across several languages over state-of-the-art baselines with relatively few additional parameters. In addition, we investigate the use of the NOS model on a 1st-pass multilingual model and show that similar to the 1st-pass model, the NOS model can be made multilingual.

Extensions and generalizations of geometric bijections for graphs

Series
Algebra Seminar
Time
Monday, September 12, 2022 - 13:30 for 1 hour (actually 50 minutes)
Location
Clough 125 Classroom
Speaker
Changxin DingGeorgia Institute of Technology

Let G be a graph. Backman, Baker, and Yuen have constructed a family of bijections between spanning trees of G and the equivalence classes of orientations up to cycle-cocycle reversal, called the geometric bijections. Their proof makes use of zonotopal subdivisions. Recently we have extended the geometric bijections to subgraph-orientation correspondences. Moreover, we have also constructed a larger family of bijections, which contains the geometric bijections and the Bernardi bijections. Most of our work is inspired by geometry but proved combinatorially.  

Resolving Matrix Spencer Conjecture Up to Polylogarithmic Rank

Series
ACO Student Seminar
Time
Monday, September 12, 2022 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haotian JiangUniversity of Washington

In this talk, I will present a simple proof of the matrix Spencer conjecture up to poly-logarithmic rank: given symmetric d by d matrices A_1,...,A_n each with operator norm at most 1 and rank at most n/\log^3 n, one can efficiently find \pm 1 signs x_1,... ,x_n such that their signed sum has spectral norm \|\sum_{i=1}^n x_i A_i\|_op= O(\sqrt{n}). This result also implies a (\log n - 3 \log \log n) qubit lower bound for quantum random access codes encoding n classical bits with advantage >> 1/\sqrt{n}. Our proof uses the recent refinement of the non-commutative Khintchine inequality in [Bandeira, Boedihardjo, van Handel, 2022] for random matrices with correlated Gaussian entries.

Tilted Planets and Black Holes: The Effect of Resonances in Some Astrophysical Systems

Series
CDSNS Colloquium
Time
Friday, September 9, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006; Zoom streaming available
Speaker
Yubo SuPrinceton University

Please Note: Zoom link: https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

In this talk, I will present the analysis of two astrophysical systems. First, exoplanets (planets orbiting a star that is not our Sun) are thought to sometimes naturally evolve into a state such that its spin axis is significantly tilted from its orbital axis. The most well-known examples of such tilts come from our own Solar System: Uranus with its 98 degree tilt is spinning entirely on its side, while Venus with its 177 degree tilt spins in the opposite direction to its orbit. I show that tilted exoplanets form probabilistically due to encountering a separatrix, and this probability can be analytically calculated using Melnikov's Method. Second, the origin of the binary black holes (BBHs) whose gravitational wave radiation has been detected by the LIGO/VIRGO Collaboration is currently not well-understood. Towards disambiguating among many proposed formation mechanisms, certain studies have computed the distributions of various physical parameters when BBHs form via certain mechanisms. A curious result shows that one such formation mechanism commonly results in black holes tilted on their sides. I show that this can be easily understood by identifying a hidden adiabatic invariant that links the initial and final spin orientations of the BBHs. No astrophysical knowledge is expected; please stop by!

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