##### Organizing Committee

- Jeffrey Hoffstein
*Brown University* - Stephen Miller
*Rutgers University* - Ramarathnam Venkatesan
*Microsoft Research India*

##### Abstract

Lattices are abstractly very simple objects, yet their concrete realizations contain beautifully intricate problems that are stubbornly difficult even in low dimensions. For example, our present day understandings of densest lattice packings and reduction theory are still plagued with large gaps.

In the 1970's and 1980's lattices entered the world of cryptography as tools used to break certain crypto systems, particularly those based on the subset sum problem, and since the 1990's they have become increasingly important in the building of other types of crypto systems (thanks to the difficulty in the underlying mathematics). Their significance has recently been bolstered by average-case complexity bounds and their present resistance to quantum computing attacks.

Currently the theory of lattices is a lively research topic among mathematicians, computer scientists, and experts in cybersecurity. However, to this date, there has been little to no interaction between these communities. The goal of this workshop is to stimulate activity between these different groups interested in lattice problems. Topics to be covered include, but are not restricted to, recent results on densest lattice packings, the geometry of lattice moduli space and its connections with automorphic forms and algebraic number theory, cryptographic applications of lattices, and the state of the art of lattice reduction in high dimensions.

#### Confirmed Speakers & Participants

- Therese Avitabile
- Boaz Barak
- Daniel J. Bernstein
- Jean-François Biasse
- Reinier Bröker
- Gizem Cetin
- Yilei Chen
- Cheng Chen
- Don Coppersmith
- Steve Damelin
- Akshay Degwekar
- Apoorvaa Deshpande
- Yarkin Doroz
- Leo Ducas
- Thomas Eisenbarth
- Lior Eldar
- Venkata Gandikota
- Farshid Hajir
- Thomas Hales
- Shai Halevi
- Nadia Heninger
- Campbell Hewett
- Jeffrey Hoffstein
- Justin Holmgren
- Seyed Kaave Hosseini
- Ewa Infeld
- Heera Janwa
- Samuel Judge
- Edmund Karasiewicz
- Saeja Kim
- Seungki Kim
- Miran Kim
- Aleksandr Kolpakov
- Gene Kopp
- Jeffrey Lagarias
- Tanja Lange
- Tianren Liu
- Linda Markowsky
- George Markowsky
- William Martin
- John Miller
- Stephen Miller
- Charles Mozzochi
- Osmanoglu Murat
- Phong Nguyen
- Daniel Nichols
- Helen Nissenbaum
- Ozgur Oksuz
- Adrian Pastine
- Chris Peikert
- Lam Pham
- Richard Pinch
- Andrew Pollington
- Thomas Prest
- Charles Radin
- Oded Regev
- James Ricci
- Sinai Robins
- Emily Russell
- Peter Sarnak
- John Schanck
- Rene Schoof
- Adam Sealfon
- Alice Silverberg
- Thomas Silverman
- Joseph Silverman
- Eric Sommers
- Noah Stephens-Davidowitz
- Sophie Stevens
- Berk Sunar
- Vladimir Tonchev
- Ha Tran
- Nicholas Triantafillou
- Douglas Ulmer
- Vinod Vaikuntanathan
- Luke Valenta
- Christine van Vredendaal
- Prashant Vasudevan
- Akshay Venkatesh
- Ian Whitehead
- Peter Winkler
- Thomas Wunderer
- Sophia Yakoubov
- Zijian Yao
- Zhuohui Zhang
- Zhenfei Zhang