NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	REGENTS OF THE UNIVERSITY OF CALIFORNIA AT RIVERSIDE
Initial Amendment Date:	August 18, 2023
Latest Amendment Date:	August 18, 2023
Award Number:	2316749
Award Instrument:	Standard Grant
Program Manager:	Adriana Salerno asalerno@nsf.gov  (703)292-2271 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	September 1, 2023
End Date:	August 31, 2025 (Estimated)
Total Intended Award Amount:	$233,452.00
Total Awarded Amount to Date:	$233,452.00
Funds Obligated to Date:	FY 2023 = $233,452.00
History of Investigator:	Patricio Gallardo Candela (Principal Investigator) pgallard@ucr.edu
Recipient Sponsored Research Office:	University of California-Riverside 200 UNIVERSTY OFC BUILDING RIVERSIDE CA  US  92521-0001 (951)827-5535
Sponsor Congressional District:	39
Primary Place of Performance:	University of California-Riverside 200 UNIVERSTY OFC BUILDING RIVERSIDE CA  US  92521-0001
Primary Place of Performance Congressional District:	39
Unique Entity Identifier (UEI):	MR5QC5FCAVH5
Parent UEI:
NSF Program(s):	LEAPS-MPS
Primary Program Source:	01002324DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):
Program Element Code(s):	217Y00
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Algebraic geometry is an area of mathematics that explores the geometry associated with the solution sets of polynomials. As the coefficients of these polynomials often vary, this, in turn, changes the geometry of their solution sets. Moreover, these geometric shapes carry linear data, known as their Hodge structures, which typically identify them. The PI will study the behavior of such geometric and linear data when these coefficients shift toward infinity. Particular focus is given to geometric cases that arise from applications to other mathematical areas like combinatorics and mathematical physics. Additionally, the researcher aims to foster an inclusive and diverse learning environment, providing students with training in geometric and computational tools, thereby empowering them to become scholars. This focus is particularly essential for first-generation students and underrepresented minorities, for whom the path to academia is often more uncertain.

This project will study GIT, Hodge theoretic, and KSBA compactifications for the moduli space of surfaces of a general type and log pairs, such as the ones associated with configurations of plane conics and log del Pezzo surfaces with their anticanonical divisors. In particular, the PI will describe well-behaved degenerations from a Hodge theory perspective and utilize techniques such as eigenspace decompositions for studying the Limiting Mixed Hodge structures of the varieties parametrized by the relevant compact moduli spaces.

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.

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