![\"Photo](\"https:\/\/www.newsbeep.com\/us-fl\/wp-content\/uploads\/2025\/12\/20251022_Mathematics_Needham-Bauer-Ozanski-Usatine_Composite_900x600.jpg\")
Clockwise from top left Tom Needham, Martin Bauer, Wojciech O\u017ca\u0144ski and Jeremy Usatine. (Devin Bittner\/FSU College of Arts and Sciences)\t\t<\/p>\n\t\tClockwise from top left Tom Needham, Martin Bauer, Wojciech O\u017ca\u0144ski and Jeremy Usatine. (Devin Bittner\/FSU College of Arts and Sciences)\t\t<\/p>\n
Four Florida State University\u00a0faculty from the\u00a0Department of Mathematics<\/a>\u00a0have\u00a0received\u00a0new funding from the\u00a0National Science Foundation\u00a0that will allow them\u00a0to\u00a0design\u00a0mathematical\u00a0mechanisms\u00a0to\u00a0improve\u00a0understanding of\u00a0theoretical\u00a0mathematical concepts,\u00a0support\u00a0students\u2019\u00a0professional\u00a0and academic growth, and develop new\u00a0methods and\u00a0tools\u00a0for use in a wide variety of applications.\u00a0<\/p>\n The three grants, totaling\u00a0more than\u00a0$500,000, were awarded\u00a0this fall\u00a0to Associate Professor of Mathematics Thomas Needham, Professor of Mathematics Martin Bauer, Assistant Professor of Mathematics\u00a0Wojciech\u00a0O\u017ca\u0144ski,\u00a0and\u00a0Assistant Professor of Mathematics Jeremy\u00a0Usatine.\u00a0<\/p>\n \u201cA common denominator in all three grants is innovation and advancement through the discovery of new, unexpected and cutting-edge results in their fields,\u201d said Ettore Aldrovandi, Department of Mathematics chair. \u201cFrom a broader point of view, their common goal is to maximize the impact their respective research activities have on the\u00a0educational\u00a0mission of the department\u00a0by supporting students, seminars and more.\u201d\u00a0<\/p>\n Projects<\/p>\n Needham and\u00a0Bauer\u00a0received a $253,888 grant for\u00a0the\u00a0project,\u00a0\u201cGeneralized Optimal Transport Models: Theory and Computation,\u201d\u00a0which will\u00a0enhance\u00a0developments\u00a0in\u00a0efficient algorithms and open-source software programs\u00a0used\u00a0in fields\u00a0ranging\u00a0from\u00a0biomedical imaging\u00a0to\u00a0artificial intelligence.\u00a0<\/p>\n The\u00a0grant, for which Needham and Bauer will collaborate\u00a0with University of Houston mathematics professor Nicolas Charon,\u00a0focuses\u00a0on optimal transport, a mathematical framework that breaks down the ideal process when moving production goods to consumers, such as estimating the correct amount of concrete needed\u00a0for a construction project\u00a0so workers don\u2019t need to transport extra materials.\u00a0\u00a0<\/p>\n \u201cOur research will provide new methods for handling complex data with additional internal structures, such as images, shapes and networks,\u201d said Needham, the project\u2019s principal investigator. \u201cSuppose you have data from a collection of arterial networks from human retinas, and you wish to\u00a0identify\u00a0features in these networks that are early indicators of a disease. Our project develops a mathematical framework for performing statistical inferences on data like this.\u201d\u00a0<\/p>\n This framework will develop\u00a0new tools that help solve fundamental problems in data science, engineering, and medical fields by strengthening systems\u2019 interpretations of visual data to improve accuracy.\u00a0\u00a0<\/p>\n O\u017ca\u0144ski\u00a0received a $145,000\u00a0grant\u00a0for\u00a0his project,\u00a0\u201cInstabilities in incompressible fluid flows,\u201d\u00a0to research how steady flows,\u00a0or fluids like air\u00a0and\u00a0fuel,\u00a0can become\u00a0unstable.\u00a0The project\u00a0aims to advance\u00a0the understanding of\u00a0the intrinsic\u00a0mechanisms of fluids, which\u00a0are\u00a0responsible for\u00a0the emergence of instabilities, and\u00a0will yield practical\u00a0results\u00a0related to\u00a0operations,\u00a0efficiency\u00a0and accuracy in areas like transportation,\u00a0energy\u00a0and weather forecasting.\u00a0<\/p>\n When a plane takes off, its wings disturb the air by creating wingtip vortices. These vortices\u00a0are highly unstable and lead to turbulent behavior\u00a0from the\u00a0air behind the plane,\u00a0a\u00a0main reason for delays\u00a0between\u00a0planes\u00a0taking\u00a0off. Understanding these\u00a0instabilities is\u00a0a\u00a0major\u00a0problem\u00a0of mathematical aerodynamics. An\u00a0analysis of\u00a0the\u00a0equations\u00a0determining\u00a0such\u00a0air\u00a0flows is crucial to the advancement of aerodynamic designs, aviation\u00a0technology\u00a0and public safety.\u00a0<\/p>\n \u201cThe project will\u00a0investigate how instabilities develop in fluids by analyzing 3D incompressible Euler equations that govern\u00a0the dynamics of inviscid fluids, or fluids\u00a0that\u00a0move with very little resistance,\u201d\u00a0O\u017ca\u0144ski\u00a0said. \u201cThe project will allow us to research new scenarios\u00a0where\u00a0steady fluid flow suddenly becomes\u00a0unstable due to disturbances,\u00a0which can lead to\u00a0unpredictable results like\u00a0reduced efficiency or turbulent behavior.\u00a0Improving our understanding of fluid instabilities\u00a0can help\u00a0improve\u00a0the efficiency of\u00a0various\u00a0energy systems\u00a0and\u00a0enhance\u00a0the technology used\u00a0for\u00a0weather predictions.\u201d\u00a0<\/p>\n Usatine\u00a0received a $108,000\u00a0grant for \u201cMotivic, Stringy, and Gromov-Witten Invariants,\u201d\u00a0through which he will\u00a0develop new tools to better understand irregular geometric spaces\u00a0and\u00a0more accurately describe their\u00a0mathematical\u00a0structures,\u00a0which are defined by equations.\u00a0<\/p>\n Usatine\u2019s\u00a0theoretical\u00a0research\u00a0focuses on\u00a0improving\u00a0the\u00a0understanding of\u00a0smooth\u00a0varieties, objects defined by equations\u00a0that appear flat\u00a0at\u00a0high magnification but\u00a0are\u00a0actually not, such as spheres.\u00a0Smooth varieties\u00a0can help explain why small system changes lead to predictable changes in a system\u2019s outcome and\u00a0are present throughout different scientific fields such as physics.\u00a0<\/p>\n His\u00a0research\u00a0also\u00a0focuses on the properties of stringy invariants \u2014 measurements that describe the structures of irregular spaces \u2014 and Gromov-Witten invariants, measurements of complex curves within a space. Invariants\u00a0don\u2019t\u00a0change even in a slightly deformed space, making them powerful tools for understanding complex geometries.\u00a0\u00a0<\/p>\n Educational Outreach\u00a0<\/p>\n Furthering\u00a0the educational mission of the department, Needham and Bauer\u2019s work\u00a0will\u00a0provide\u00a0opportunities for students\u00a0through\u00a0Python\u00a0coding courses\u00a0for graduate students and junior researchers\u00a0and K-12 student outreach activities.\u00a0The four\u00a0faculty\u00a0members\u00a0from\u00a0each\u00a0grant all\u00a0plan to organize activities related to their\u00a0projects\u00a0to\u00a0exhibit\u00a0at\u00a0FSU\u00a0Math Fun Day<\/a>, an annual outreach event that engages K-12 students with hands-on activities\u00a0each February.\u00a0<\/p>\n