NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF ILLINOIS
Initial Amendment Date:	May 8, 2017
Latest Amendment Date:	May 8, 2017
Award Number:	1719242
Award Instrument:	Standard Grant
Program Manager:	Joanna Kania-Bartoszynska jkaniaba@nsf.gov  (703)292-4881 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2017
End Date:	June 30, 2018 (Estimated)
Total Intended Award Amount:	$45,000.00
Total Awarded Amount to Date:	$45,000.00
Funds Obligated to Date:	FY 2017 = $45,000.00
History of Investigator:	Vesna Stojanoska (Principal Investigator) vesna@illinois.edu Charles Rezk (Co-Principal Investigator) Mark Johnson (Co-Principal Investigator) Daniel Davis (Co-Principal Investigator)
Recipient Sponsored Research Office:	University of Illinois at Urbana-Champaign 506 S WRIGHT ST URBANA IL  US  61801-3620 (217)333-2187
Sponsor Congressional District:	13
Primary Place of Performance:	University of Illinois at Urbana-Champaign 1901 South First Street CHAMPAIGN IL  US  61820-7473
Primary Place of Performance Congressional District:	13
Unique Entity Identifier (UEI):	Y8CWNJRCNN91
Parent UEI:	V2PHZ2CSCH63
NSF Program(s):	TOPOLOGY
Primary Program Source:	01001718DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):	7556
Program Element Code(s):	126700
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

The week-long, international conference "Homotopy theory: Tools and Applications" will be held at the University of Illinois at Urbana-Champaign, July 17-21, 2017. The primary goal of the conference is to provide a platform for building on recent developments in homotopy theory, especially its growth in the Midwest. This will be accomplished in several ways, primarily by allowing a carefully selected group of 20 international experts to share cutting-edge results and discoveries via hour-long plenary talks spaced throughout the week. There will also be a series of talks scheduled in parallel sessions and presented by volunteers, allowing young people, those from underrepresented groups, and those from smaller institutions to present their recent work to this focused audience. In addition, various efforts will be made to create an environment conducive to fostering new interactions and the development of future collaborations.

In the past decade or so, the subject of homotopy theory has seen a remarkable amplification of its scope. Already a mature subject, the ideas and methods of homotopy theory have been applied to diverse areas (sometimes under the guise of infinity-category theory), including algebraic and differential geometry, algebraic K-theory and motivic homotopy theory, mathematical physics, and representation theory (sometimes incorporating all of the above). In addition, the techniques of algebraic topology have been built into methods for analyzing large data sets, with applications in sensing and medicine. The 20 plenary talks at the conference will be given by speakers whose work in developing tools of abstract, equivariant, or chromatic homotopy theory has contributed to the aforementioned varied applications of homotopy theory in other areas.

More information about the conference is available at http://www.math.illinois.edu/homotopy2017/index.html

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.

In the past decade or so, the subject of homotopy theory has seen a remarkable amplification of its scope. With a number of recent faculty moves to permanent positions in the Midwest, its role as a geographic center for homotopy theory within the United States as well as worldwide has been reinforced. 

The primary goal of the sponsored conference was to provide a platform for building on the recently increased strengths of both the region and the content area. 

 

Intellectual merit: The conference talks showcased recent advances in homotopy theory and more generally the applications of its methods to other areas, such as geometry and arithmetic. Structural as well as computational results were presented, including many of chromatic, equivariant, K-theoretic, and motivic flavors.

 

Broader impacts: The grant funded 91 conference attendees, 60% of whom were graduate students, and 20% postdocs, to enable them to participate in this major event in the field of homotopy theory.

At the conference, and in addition to the 20 plenary talks, 24 participants contributed shorter talks in parallel sessions. Further, there was a collaboration session evening, in which experts led small-group discussions on open problems in their area, in order to foster new collaborations among participants at various stages in their career.

Last Modified: 10/09/2018
Modified by: Vesna Stojanoska

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