Maneesha Ampagouni

Maneesha Ampagouni

PhD Candidate in Mathematics

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Posts

Future Blog Post

less than 1 minute read

This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.

Blog Post number 4

less than 1 minute read

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

less than 1 minute read

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 2

less than 1 minute read

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 1

less than 1 minute read

This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

publications

Paper Title Number 4

This paper is about fixing template issue #693.

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
Download Paper

talks

Vertex Operator Algebra Theory Reading Group

Overview:
I organized this reading group on vertex operator algebras with two other members of my department at University of California, Santa Cruz. This reading group aims to deepen our understanding of concepts in VOA theory through regular discussions and presentations.

Introduction to Monstrous Moonshine

Abstract: In 1978, mathematician John McKay made a remarkable observation that ignited a series of captivating discoveries and conjectures, revealing unexpected connections between finite group theory and modular forms. This phenomenon, as it unfolded, was dubbed “moonshine” by John H. Conway, capturing the mysterious and intriguing nature of the emerging correspondence. In my talk, I will delve into the journey of exploration spurred by these conjectures. Central to our exploration is the discovery of a structure from physics that serves as a bridge between finite group theory and modular forms. I will elucidate how this unexpected connection sheds light on the mathematical origin of these structures and served as a motivation to study them.

Z2-orbifold of a Lattice VOA

Abstract: A well-known example of a vertex operator algebra (VOA) is the Moonshine module, whose connection to the j-function and the Monster group revealed a surprising link between group theory and modular forms. The construction of the moonshine module can be generalized by replacing the Leech lattice with any even lattice, resulting in the $\mathbb{Z}_2$-orbifold of a lattice VOA, which still exhibits modular invariance. In this talk, I will introduce VOAs and the construction of a $\mathbb{Z}_2$-orbifold of a lattice VOA. The goal of this colloquium is to lay the groundwork for understanding the computation of 1-point functions in such an orbifold, which will be discussed in detail in the algebra and number theory seminar later this week.

1-Point Functions for Z2-orbifolds of Lattice VOAs

Abstract: The Moonshine module, a vertex operator algebra (VOA) linking the Monster group to modular forms via the j-function, has inspired significant research into VOAs and their modular properties. One way to explore and understand the modular properties of VOAs is through their 1-point functions. In this talk, I will present my work on computing the 1-point functions for the $\mathbb{Z}_2$-orbifolds of lattice VOAs. I will begin by introducing the standard Zhu theory, followed by an explanation of how Mason and Mertens developed the $\mathbb{Z}_2$-twisted Zhu theory to compute the 1-point functions in the untwisted sector for symmetrized Heisenberg and lattice VOAs. I will then show how I extended these techniques to perform computations in the twisted sector. This allowed me to derive the 1-point functions for the $\mathbb{Z}_2$-orbifold, which, as expected, are level-one modular forms for the full modular group $SL_2(\mathbb{Z})$, up to a character.

teaching