Seminars and Colloquia by Series

Cancelled

Series
Analysis Seminar
Time
Wednesday, April 22, 2020 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker

Finding and cerifying roots of systems of equations

Series
Dissertation Defense
Time
Tuesday, April 21, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://gatech.bluejeans.com/481175204
Speaker
Kisun Lee – Georgia Tech –

Numerical algebraic geometry studies methods to approach problems in algebraic geometry numerically. Especially, finding roots of systems of equations using theory in algebraic geometry involves symbolic algorithm which requires expensive computations, numerical techniques often provides faster methods to tackle these problems. We establish numerical techniques to approximate roots of systems of equations and ways to certify its correctness.

As techniques for approximating roots of systems of equations, homotopy continuation method will be introduced. Combining homotopy method with monodromy group action, we introduce techniques for solving parametrized polynomial systems. Since numerical approaches rely on heuristic method, we study how to certify numerical roots of systems of equations. Based on Newton’s method, we study Krawczyk method and Smale’s alpha theory. These two method will be mainly used for certifying regular roots of systems. Furthermore, as an approach for multiple roots, we establish the local separation bound of a multiple root. For multiple roots whose deflation process terminates by only one iteration, we give their local separation bound and study how to certify an approximation of such multiple roots.

 

All lines on a smooth cubic surface in terms of three skew lines

Series
Algebra Seminar
Time
Monday, April 20, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tianyi Zhang – Georgia Tech –
Harris showed that the incidence variety of a smooth cubic surface containing 27 lines has solvable Galois group over the incidence variety of a smooth cubic surface containing 3 skew lines. It follows that for any smooth cubic surface, there exist formulas for all 27 lines in terms of any 3 skew lines. I will briefly talk about Harris' results and how Stephen, Daniel, and I compute these formulas explicitly.
 

The talk will be held online via Bluejeans, use the following link to join the meeting.

TBA by Jeffrey Rosenthal

Series
Combinatorics Seminar
Time
Friday, April 17, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeffrey Rosenthal – University of Toronto

TBA (joint with Stochastics Seminar)

Spectrum Reconstruction Technique and Improved Naive Bayes Models for Text Classification Problems

Series
Dissertation Defense
Time
Thursday, April 16, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Bluejeans Meeting 866242745
Speaker
Zhibo Dai – Georgia Tech –

My thesis studies two topics. In the first part, we study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA (Principal Component Analysis). We believe that related algorithms should perform better with more accurate spectrum estimation. There was an approximation formula proposed by Prof. Matzinger. However, they didn't give any proof. In our research, we show why the formula works. And when both number of features and dimension of space go to infinity, we find the order of error for the approximation formula, which is related to a constant C-the ratio of dimension of space and number of features.

In the second part, we focus on some applications of Naive Bayes models in text classification problems. Especially we focus on two special situations: 1) there is insufficient data for model training; 2) partial labeling problem. We choose Naive Bayes as our base model and do some improvement on the model to achieve better performance in those two situations. To improve model performance and to utilize as many information as possible, we introduce a correlation factor, which somehow relaxes the conditional independence assumption of Naive Bayes. The new estimates are biased estimation compared to the traditional Naive Bayes estimate, but have much smaller variance, which give us a better prediction result.

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