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I am a PhD student in number theory at Louisiana State University.
My research interests are in exponential sums, character sums and their applications. My advisor is Prof. Ling Long. Office: 355 Lockett Hall Department of Mathematics Louisiana State University Baton Rouge, 70803 Email: lngu145 AT lsu.edu |
Research:
On Weil Sums, Conjectures of Helleseth and Niho Exponents, submitted for publication.
https://arxiv.org/abs/2006.15726.
In this project studied I invested conjectures made by Tor Helleseth in 1971 about the Weil sum, a finite field character sum of binomials. The number of distinct elements that this sum takes over invertible elements in the field is called the Weil spectrum. My recent work includes giving a proof to one of the Helleseth conjectures in the case of Niho exponents, and based on numerical data, proposing a new conjecture concerning the Weil spectrum of at least five elements, and giving some partial progress towards this.
The Weil sum has different applications in cryptography, coding and information theory.
Conferences:
Teaching:
This semester I am teaching Math 1551 Honors Calculus I.
I have taught the following courses at LSU:
I have also taught: Mthsc 1020 (Fall 2012) Business Calculus I and Mthsc 2070 (Spring 2013, 2014, 2015, Fall 2013, 2014) at Clemson University.
Apart from teaching, I have been a teaching assistant to: Math 7210 Graduate Abstract Algebra (Fall 2016), Math 4200 Undergraduate Abstract Algebra (Fall 2016), Math 4181 Number Theory (Fall 2015), Math 2085 Linear Algebra (Fall 2015), Math 2057 Multivariable Calculus (Spring 2018, Fall 2017, Spring 2017, Spring 2016), Math 1552 Calculus II (Spring 2016), and Math 1100 Nature of Mathematics (Fall 2017).
Other Academic Activities:
On Weil Sums, Conjectures of Helleseth and Niho Exponents, submitted for publication.
https://arxiv.org/abs/2006.15726.
In this project studied I invested conjectures made by Tor Helleseth in 1971 about the Weil sum, a finite field character sum of binomials. The number of distinct elements that this sum takes over invertible elements in the field is called the Weil spectrum. My recent work includes giving a proof to one of the Helleseth conjectures in the case of Niho exponents, and based on numerical data, proposing a new conjecture concerning the Weil spectrum of at least five elements, and giving some partial progress towards this.
The Weil sum has different applications in cryptography, coding and information theory.
Conferences:
- (Invited Talk) AMS Fall Southeastern Sectional Meeting, Special Session on Experimental Mathematics in Number Theory and Combinatorics, University of Florida, Gainesville, FL, November 2019.
- MSRI Summer School on Toric Varieties, National Center for Theoretical Sciences, Taipei, Taiwan, July-August 2019.
- (Invited Talk) Arithmetic of Function Fields and Diophantine Geometry, National Center for Theoretical Sciences, Taipei, Taiwan, May 2019.
- Southern Regional Number Theory Conference, Louisiana State University, Baton Rouge, LA, April 2019.
- (Contributed Talk) Texas-Oklahoma Representations and Automorphic Forms X, University of North Texas, Denton, TX, April 2019.
- Connecticut Summer School in Number Theory Research Conference, University of Connecticut, Storrs, CT, June 2018.
- Strength in Numbers, Queen's University, Kingston, Canada, May 2018.
- Positivity in Arithmetic and Geometry, Universite Paris-Sud, Orsay, France, May 2017.
- Texas Algebraic Geometry Symposium, Rice University, Houston, TX, April 2017.
- Southern Regional Number Theory Conference, Louisiana State University, Baton Rouge, LA, April 2017.
Teaching:
This semester I am teaching Math 1551 Honors Calculus I.
I have taught the following courses at LSU:
- Math 1552 Calculus II, Spring 2020.
- Math 1550 Calculus I, Fall 2019.
- Math 1022 Trigonometry, Spring 2019.
- Math 1021 College Algebra, Fall 2018.
I have also taught: Mthsc 1020 (Fall 2012) Business Calculus I and Mthsc 2070 (Spring 2013, 2014, 2015, Fall 2013, 2014) at Clemson University.
Apart from teaching, I have been a teaching assistant to: Math 7210 Graduate Abstract Algebra (Fall 2016), Math 4200 Undergraduate Abstract Algebra (Fall 2016), Math 4181 Number Theory (Fall 2015), Math 2085 Linear Algebra (Fall 2015), Math 2057 Multivariable Calculus (Spring 2018, Fall 2017, Spring 2017, Spring 2016), Math 1552 Calculus II (Spring 2016), and Math 1100 Nature of Mathematics (Fall 2017).
Other Academic Activities:
- In summer 2019 I had a research visit at the National Center for Theoretical Sciences in Taipei, Taiwan.
- In spring 2019 I co-organized the Southern Regional Number Theory Conference on "Modular Forms, Modular Curves and Hypergeometric Functions" at Louisiana State University in Baton Rouge, LA.
- I co-run a weekly Student Number Theory Seminar at LSU.
