##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Prasuna Bandi

#### Tata Institute of Fundamental Research

## Density at integer points of an inhomogeneous quadratic form and linear form

##### Abstract:

In 1987, Margulis solved an old conjecture of Oppenheim which states that for a nondegenerate, indefinite and irrational quadratic form $Q$ in $n \geq 3$ variables, $Q(\mathbb{Z}^n)$ is dense in $\mathbb{R}$. Following this, Dani and Margulis proved the simultaneous density at integer points for a pair consisting of quadratic and linear form in $3$ variables when certain conditions are satisfied. We prove an analogue of this for the case of an inhomogeneous quadratic form and a linear form. \\ \\ This is based on joint work with Anish Ghosh.

Host: Brandon Seward

### April 27, 2021

### 10:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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