NSF Award Search: Award # 1953687

Award Abstract # 1953687

Periodic Kardar-Parisi-Zhang (KPZ) Universality

NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF KANSAS CENTER FOR RESEARCH INC
Initial Amendment Date:	January 17, 2020
Latest Amendment Date:	January 17, 2020
Award Number:	1953687
Award Instrument:	Standard Grant
Program Manager:	Tomek Bartoszynski tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2020
End Date:	June 30, 2024 (Estimated)
Total Intended Award Amount:	$168,627.00
Total Awarded Amount to Date:	$168,627.00
Funds Obligated to Date:	FY 2020 = $168,627.00
History of Investigator:	Zhipeng Liu (Principal Investigator) zhipeng@ku.edu
Recipient Sponsored Research Office:	University of Kansas Center for Research Inc 2385 IRVING HILL RD LAWRENCE KS US 66045-7563 (785)864-3441
Sponsor Congressional District:	01
Primary Place of Performance:	University of Kansas Center for Research Inc 2385 Irving Hill Road Lawrence KS US 66045-7568
Primary Place of Performance Congressional District:	01
Unique Entity Identifier (UEI):	SSUJB3GSH8A5
Parent UEI:	SSUJB3GSH8A5
NSF Program(s):	PROBABILITY
Primary Program Source:	01002021DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):	9150
Program Element Code(s):	126300
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Many random growth models, such as fire propagation or bacterial colony growth are believed to share certain universal pattern. Analyzing the mathematical mechanism of such pattern has been an active research area in the last twenty years. Due to the breakthrough progress in the probability and mathematical physics community, an increasing number of models have been successfully analyzed and they are found to share the same large time limiting behaviors. These models are called to belong to the Kardar-Parisi-Zhang (KPZ) universality class, named after Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang who introduced a non-linear stochastic partial differential equation, the so-called KPZ equation, to describe the random growing interfaces.

This project aims to study models in the KPZ universality class with spatial periodicity. One goal of this project is to analyze the periodic solvable growth models and understand their universal limiting behaviors under different parameter scales by probing the structure and asymptotics of the Bethe roots associated with these models. The other goal is to develop a new direction to approach the KPZ universality class in the infinite space by obtaining exact results of periodic solvable growth models when the period becomes sufficiently large.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Baik, Jinho and Liu, Zhipeng and Silva, Guilherme L. "Limiting one-point distribution of periodic TASEP" Annales de l'Institut Henri Poincaré, Probabilités et Statistiques , v.58 , 2022 https://doi.org/10.1214/21-AIHP1171 Citation Details

Liu, Zhipeng "One-point distribution of the geodesic in directed last passage percolation" Probability Theory and Related Fields , 2022 https://doi.org/10.1007/s00440-022-01123-2 Citation Details

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

Award title: Periodic Kardar-Parisi-Zhang (KPZ) Universality

Award number: 1953687
PI: Zhipeng Liu

In 2020, the PI (Zhipeng Liu) received the NSF award "Periodic Kardar-Parisi-Zhang (KPZ) Universality", with the award amount $168,627.00. With the support, the PI was able to make significant progress toward the project on the periodic KPZ university. There are three main outcomes from this project.

First, PI made important contributions in understanding the periodic KPZ universality during the period of support. There have been breakthrough results on the universal limiting fields, namely the KPZ fixed point and the directed landscape, of some integrable random growth models. Previously, the PI and his collaborators were able to find exact formulas of the periodic analog of the KPZ fixed point, which we called the periodic KPZ fixed point. The PI was able to extend his earlier results on the random growth models on a periodic domain to the full space, and obtained some new formulas and used them to find new properties of the KPZ fixed point. The PI and his collaborators also discovered some new properties of the periodic KPZ fixed point.

Secondly, the PI actively introduced his new results to other researchers and students by giving many talks at conferences and seminars, and providing many problems to graduate students. The PI also invited many young researchers to KU probability and statistics seminar and exchanged problems and ideas during the visits. All these activities helped increase the broader impact of this direction in the probability area and in general mathematics.

Finally, one participant of the project Ray Zhang, the PI's first graduate student, received a lot of travel and research support from the award. He recently successfully defended his PhD thesis. He is now a named postdoc at the University of Utah. The PI also used the award to support his second graduate student, who is still making progress toward graduation. So the award has a very positive educational impact in mathematics.

Last Modified: 07/30/2024
Modified by: Zhipeng Liu

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