Physical mathematics is concerned with mathematics motivated by physics. Prime example of physical mathematics is the pioneering work of Eugene Wigner on the unitary representations of Poincare group which was motivated by his results proving that symmetries of quantum systems must be realized unitarily on their Hilbert spaces. His work opened up the huge field studying the unitary duals of noncompact Lie groups which is still an unfinished chapter of mathematics. In a similar vein, the discovery of supersymmetry by physicists led to the development of the theory of unitary representations of Lie superalgebras. Remarkably, though algebraically more complicated the theory of unitary representations of noncompact Lie superalgebras turned out to be simpler than those of noncompact Lie groups. Furthermore, some of the earliest results on AdS/CFT dualities were obtained, in a true Wignerian sense, within the framework of work on fitting the spectra of Kaluza-Klein supergravities into unitary supermultiplets of their underlying supersymmetry algebras.
IGC members who study Physical Mathematics
|Name||Role||Affiliation||Phone||Office Address||Affiliated Center(s)||Research Topics(s)|
|Allison Colarelli||Undergraduate Student||Math, Astronomyfirstname.lastname@example.org||7175982124||N/A NONE||IGC, CFT||Gravitational Waves, Loop Quantum Gravity, Physical Mathematics, Black Holes|
|Aurora Colter||Undergraduate Student||Physics, Mathemail@example.com||-||- NONE||CFT, IGC||Physical Mathematics, Black Holes, Gravitational Waves, Loop Quantum Gravity, Quantum Universe|
|Murat Gunaydin||Faculty||Physicsfirstname.lastname@example.org||+1 814 863 0144||303F Osmond Laboratory||CFT||Physical Mathematics|
|Daniel Paraizo||Graduate Student||Physicsemail@example.com||--||114 Osmond Laboratory||CFT, IGC||Physical Mathematics, Quantum Universe, Black Holes, Loop Quantum Gravity|
News about Physical Mathematics
NASA selects STAR-X for $3M mission concept study
STAR-X, the Survey and Time-domain Astrophysical Research Explorer, a proposed NASA Medium-Class Explorer (MIDEX) mission that includes Penn State astronomer Niel Brandt, has been selected by the NASA Explorers Program for further study. STAR-X is one of two proposed MIDEX missions that will receive $3 million for a nine-month detailed study of mission requirements. At the end of this period, one of the proposed missions will be selected for a target launch date in 2027-2028 and be eligible for up to $300 million in additional funding.
Comprised of an X-ray telescope, an ultraviolet (UV) telescope, and a responsive spacecraft, STAR-X is designed to conduct time-domain surveys, which study how astronomical objects change with time, and to respond rapidly to transient cosmic events discovered by other observatories such as LIGO, Rubin LSST, the Roman Space Telescope, and the Square Kilometer Array. The mission is led by Principal Investigator William Zhang at NASA’s Goddard Space Flight Center (GSFC) in Greenbelt, Maryland. Penn State’s Brandt, who is the Verne M. Willaman Professor of Astronomy and Astrophysics and Professor of Physics, is involved in planning the STAR-X cosmic X-ray surveys, active galaxy studies, and fast X-ray transient studies.
“I can’t wait to use STAR-X to investigate the first supermassive black holes and understand mysterious, explosive X-ray transient sources,” said Brandt. “STAR-X will also provide the essential X-ray and UV follow-up capabilities for remarkable cosmic objects discovered by the Rubin LSST in optical light.”
The STAR-X spacecraft would be able to turn rapidly to point a sensitive wide-field X-ray telescope and a UV telescope at transient cosmic sources, such as supernova explosions and feeding supermassive black holes. Deep X-ray surveys would map black holes and hot gas trapped in distant clusters of galaxies; combined with infrared observations from NASA’s upcoming Roman Space Telescope, these observations would trace how massive clusters of galaxies built up over cosmic history.
STAR-X would provide revolutionary capabilities including unprecedented X-ray and UV volumetric survey speed; a unique combination of large field-of-view, large X-ray collecting area, low background, and excellent imaging; increased sensitivity for characterizing diffuse emissions, and increased speed and sensitivity for the discovery of faint X-ray point sources. It fills the gap in X-ray and UV survey coverage, providing simultaneous X-ray and UV observations, which are among the earliest and most uniquely informative astrophysical signals that probe the inner regions around compact objects like black holes and neutron stars, and it complements optical, infrared, and gravitational wave facilities.
The mission’s Deputy Principal Investigator, Ann Hornschemeier, who is also Lab Chief for X-ray Astrophysics at GSFC, earned a Ph.D. in Astronomy and Astrophysics at Penn State, mentored by Brandt, in 2002.
“Ann is superb - a bundle of energy, and the right person to push STAR-X to succeed,” said Brandt.
NASA Explorer missions conduct focused scientific investigations and develop instruments that fill scientific gaps between the agency’s larger space science missions. The proposals were competitively selected based on potential science value and feasibility of development plans. The Explorers Program is the oldest continuous NASA program and is designed to provide frequent, low-cost access to space using principal investigator-led space science investigations relevant to the Science Mission Directorate’s astrophysics and heliophysics programs.
“NASA’s Explorers Program has a proud tradition of supporting innovative approaches to exceptional science, and these selections hold that same promise,” said Thomas Zurbuchen, associate administrator for NASA’s Science Mission Directorate at NASA Headquarters in Washington. “From studying the evolution of galaxies to explosive, high-energy events, these proposals are inspiring in their scope and creativity to explore the unknown in our universe.”
Since the launch of Explorer 1 in 1958, which discovered the Earth’s radiation belts, the Explorers Program has launched more than 90 missions, including the Uhuru and Cosmic Background Explorer (COBE) missions that led to Nobel prizes for their investigators.
The program is managed by NASA Goddard for NASA’s Science Mission Directorate in Washington, which conducts a wide variety of research and scientific exploration programs for Earth studies, space weather, the solar system, and the universe. More information can be found at the Explorers Program website (https://explorers.gsfc.nasa.gov/).
Further technical details about the observatory are available at (http://star-x.xraydeep.org/observatory/).