Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
Discovery And Development Of Better Pain Treatments
Funder
National Health and Medical Research Council
Funding Amount
$9,613,850.00
Summary
Many forms of pain remain poorly treated, leading to significant quality of life and economic losses. This Program grant will discover and characterise new peptides from cone snails and spiders that modulate specific channels in nerves that are critical to the transmission of pain signals to the brain. Using advanced chemical and structural approaches, promising leads will be optimised for potency and stability and evaluated in disease and pathway-specific models of pain to establish their clini ....Many forms of pain remain poorly treated, leading to significant quality of life and economic losses. This Program grant will discover and characterise new peptides from cone snails and spiders that modulate specific channels in nerves that are critical to the transmission of pain signals to the brain. Using advanced chemical and structural approaches, promising leads will be optimised for potency and stability and evaluated in disease and pathway-specific models of pain to establish their clinical potential.Read moreRead less
GABA(B) Receptor Modulation Of Gastrointestinal Function In Health And Disease By Alpha-Conotoxins
Funder
National Health and Medical Research Council
Funding Amount
$689,050.00
Summary
Chronic visceral pain is a common and debilitating condition arising from numerous diseases that affect our internal organs. There is a desperate need for more information about the mechanisms responsible for signalling chronic visceral pain to provide therapies and potentially find a cure for it. Our research focuses on ?-conotoxins (small peptides from marine cone snail venom) as novel potential therapeutic agents for the treatment of chronic visceral pain.
Transient Receptor Potential Channels (TRPs) As Transducers And Targets In Primary Visceral Afferents
Funder
National Health and Medical Research Council
Funding Amount
$669,130.00
Summary
Transient receptor potential, or TRP channels, are involved in generating many of the sensations we perceive, such as heat, cold, touch and pain. Some TRP channels are specialized to signal pain from visceral organs, which we must investigate if we are to find treatments for visceral pain, which are currently lacking.
Discovery Early Career Researcher Award - Grant ID: DE140100633
Funder
Australian Research Council
Funding Amount
$395,169.00
Summary
Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations ....Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations of affine Kac-Moody algebras at the critical level.Read moreRead less