Inside UT Math
Recognition of Faculty and Graduate Students
The Department of Mathematics is pleased to announce the recipients of the Frank Gerth III Teaching Excellence Awards and the Department of Mathematics Outstanding Teaching Awards for 2007-2008. Heather Van Ligten and Diane Radin are the recipients of Department of Mathematics Outstanding Teaching Award. Herivelto Borges Filho, Kris Clabes, Eric Staron, Brandy Guntel and Pippa Charters are the recipients of Frank Gerth III Teaching Excellence Award. Allison Bishop, Jin Hyuk Choi Yuan Yao and Kyudong Choi are the recipients of Frank Gerth III Graduate Excellence Award. Ricado Alonso, Magda Czubak, Alex Kahle, Mark Luxton and Andrea Young are the recipients of Frank Gerth III Dissertation Awards.
The Department of Mathematics is pleased to announce the recipients of the Frank Gerth III Teaching Excellence Awards and the Department of Mathematics Outstanding Teaching Awards for 2007-2008. Heather Van Ligten and Diane Radin are the recipients of Department of Mathematics Outstanding Teaching Award. Herivelto Borges Filho, Kris Clabes, Eric Staron, Brandy Guntel and Pippa Charters are the recipients of Frank Gerth III Teaching Excellence Award. Allison Bishop, Jin Hyuk Choi Yuan Yao and Kyudong Choi are the recipients of Frank Gerth III Graduate Excellence Award. Ricado Alonso, Magda Czubak, Alex Kahle, Mark Luxton and Andrea Young are the recipients of Frank Gerth III Dissertation Awards.Mathematics New Faculty
The Department of Mathematics would like to welcome all of our new faculty and students. Thirteen new faculty members, Jane Arledge, Clayton Bjorland, Gerard Brunick, Chi Han Chan, Thomas Chen, David Fithian, John Hammond, Florent Jouve, Hector Lomeli, Brett Milburn, Hossein Namazi, Kui Ren and Stephanie Somersille have joined the department this fall.
The Department of Mathematics would like to welcome all of our new faculty and students. Thirteen new faculty members, Jane Arledge, Clayton Bjorland, Gerard Brunick, Chi Han Chan, Thomas Chen, David Fithian, John Hammond, Florent Jouve, Hector Lomeli, Brett Milburn, Hossein Namazi, Kui Ren and Stephanie Somersille have joined the department this fall.
Emerging Scholars
The Emerging Scholars Program is a nationally known program
for furthering the education of students from
non-traditional backgrounds. Students from high schools with
a weak mathematics program find themselves challenged by the
demands of an honors environment. And, they succeed in
Mathematics as well as in the University.
The Emerging Scholars Program is a nationally known program
for furthering the education of students from
non-traditional backgrounds. Students from high schools with
a weak mathematics program find themselves challenged by the
demands of an honors environment. And, they succeed in
Mathematics as well as in the University.
Education In Texas
UT Austin provides leadership for educators in Texas,
assisting communities with primary, middle school and
secondary education.
Under the direction of nationally
recognized Mathematics Professor Uri Treisman, the Dana
Center for Education Research has led the state in reforming
school curriculum.
UT Austin provides leadership for educators in Texas,
assisting communities with primary, middle school and
secondary education.
Under the direction of nationally
recognized Mathematics Professor Uri Treisman, the Dana
Center for Education Research has led the state in reforming
school curriculum.
Community Outreach
About every fourth Saturday, high school students from across the
state meet to get down with Mathematics. The Saturday
Morning Math Group was begun by Mathematics Professor Karen
Uhlenbeck and Dan Freed in fall 1993, and is now a popular outreach program
bringing extra-curricular education to students across the
state.
About every fourth Saturday, high school students from across the
state meet to get down with Mathematics. The Saturday
Morning Math Group was begun by Mathematics Professor Karen
Uhlenbeck and Dan Freed in fall 1993, and is now a popular outreach program
bringing extra-curricular education to students across the
state.
Around UT Austin
- Professor Elizabeth Warnock Fernea diesNoted author, who taught for 24 years at UT, championed women's issues in Middle East.
- $3 million awarded for principal trainingCollege of Education gets U.S. Department of Education funds for inner-city school program.
- Center named for former Gov. Dolph BriscoeCenter for American History gets $15 million in gifts from advocate of history preservation.
- Discovery reveals how plants grow biggerChanges in internal clocks give hybrid plants, such as corn, more vigor than their parents.
- Scientists find hidden glaciers on MarsResearchers uncover vast deposits of water on planet, renewing hopes for life in space.
| Sun | Mon | Tue | Wed | Thu | Fri | Sat |
| 30 | 1
2:00p RLM 12.166 Topology
John Berge: On locating and identifying minimal complexity genus two Heegaard diagrams of compact, closed, orientable 3-manifolds. 3:00p RLM 10.176 Jr Analysis Veronica Quitalo: Some Results on Fully Nonlinear Equations 3:00p RLM 9.166 Math Finance Huyên PHAM: Optimal portfolio/consumption choice in a liquidity risk model with random trading dates | 2
12:30p RLM 9.166 GADGET
Christoph Sachse: Comparing infinity-categories with topological and simplicial categories 2:00p RLM 9.166 Algebra, Number Theory, & Combinatorics Federico Ardila: Combinatorics and geometry of power ideals | 3
1:00p RLM 10.176 Analysis
Ricardo Alonso: The Boltzmann collision operator: Classical estimates using radial symmetrization techniques and applications 2:00p RLM 11.176 Numerical Analysis Lexing Ying: Butterfly Algorithm and Its Applications 3:00p RLM 9.166 Special Andrew Gillette: Applications of the Hodge Decomposition to Biological Structure and Function Modeling 4:00p RLM 10.176 Working Dynamical Systems Michael Ortiz: Group Representations in Quantum Field Theory 5:00p RLM 12.104 umrg: Math Club Cody Patterson: Spherical Geometry: Methods and Magic | 4
2:00p RLM 9.166 Algebra, Number Theory, & Combinatorics
Matt Young: Quadratic twists of a modular L-function 3:30p RLM 9.166 Geometry TBA: TBA | 5
10:30a GSB 3.138 Joint Math IROM
Mark Schroder: Optimal debt contracts and product market competition with exit and entry 1:00p RLM 10.176 Analysis Alessio Figalli: Regularity results for optimal transport maps on Riemannian manifolds 1:30p RLM 9.166 Probability Steven Shreve: Double Skorokhod Map and Reneging Real-Time Queues 2:00p ACE 6.304 ICES Gustavo Gioia : Nikuradse meets Kolmogorov, or: How to derive the diagram from the spectrum | 6 |
| 7 | 8 | 9
12:30p RLM 9.166 Special
Ronny Hadani: Group Representation Patterns in Digital Signal Processing 3:30p ACES 6.304 Appl Math/ICES Lect Pierre-Louis Lions: An Introduction to Mean Field Game Models 4:00p 10.176 Working Dynamical Systems Craig Michoski: Nonlinear PDEs, finite elements and universal attractors. | 10 | 11
3:30p RLM 9.166 No Geometry will be held this week.
| 12 | 13 |
| 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 |
| 28 | 29 | 30 | 31 | 1 | 2 | 3 |
Events Today
10:30a GSB 3.138 Joint Math IROM
Mark Schroder: Optimal debt contracts and product market competition with exit and entry 10:30 am in GSB 3.138 Joint Math IROM
Optimal debt contracts and product market competition with exit and entry
Mark Schroder (Michigan State University)
We show that optimal debt contracts in the presence of product market competition are typically different from standard debt contracts. We consider a market with two incumbents, one levered (target) and one with deep pockets (competitor). Renewal of target's debt depends on its profits, which are determined by the competitor's pricing strategy. When the competitor benefits from non-renewal of target's debt, it has incentive to price more aggressively. To counter this, bondholders make renewal less profit sensitive, and the optimal debt contract is smooth (nonkinked) and concave, and lies below the standard debt contract. Bondholders leave the limited liability constraint slack in a region of profits, and therefore appear to leave money on the table by failing to collect all profits when they fall short of the debt's face value. But this flattening of the contract results in higher profits for the levered firm for each state of demand, and a higher expected payout for bondholders. The larger the competitor's benefit from non-renewal, the flatter the contract. On the other hand, when the competitor benefits from renewal of the target's debt (say non-renewal results in target's replacement by a more efficient entrant), then the optimal debt contract is nonsmooth (sometimes taking the form of a binary option), and much more profit sensitive for some profit levels than the standard contract. This increased sensitivity amplifies the competitor's incentive to price less aggressively, resulting in higher profits for the levered firm and higher payout to bondholders. In either case, our results demonstrate the optimal contract must be designed accounting for the impact of the contract itself on the profit function of the levered firm. Furthermore, bondholders prefer lending to weaker firms (firms whose competitors benefit from renewal) because the competitor's pricing incentive, amplified by the more profit sensitive contract, results in higher expected payouts.
Submitted by sirbu@math.utexas.edu
Mark Schroder: Optimal debt contracts and product market competition with exit and entry 10:30 am in GSB 3.138 Joint Math IROM
Optimal debt contracts and product market competition with exit and entry
Mark Schroder (Michigan State University)
We show that optimal debt contracts in the presence of product market competition are typically different from standard debt contracts. We consider a market with two incumbents, one levered (target) and one with deep pockets (competitor). Renewal of target's debt depends on its profits, which are determined by the competitor's pricing strategy. When the competitor benefits from non-renewal of target's debt, it has incentive to price more aggressively. To counter this, bondholders make renewal less profit sensitive, and the optimal debt contract is smooth (nonkinked) and concave, and lies below the standard debt contract. Bondholders leave the limited liability constraint slack in a region of profits, and therefore appear to leave money on the table by failing to collect all profits when they fall short of the debt's face value. But this flattening of the contract results in higher profits for the levered firm for each state of demand, and a higher expected payout for bondholders. The larger the competitor's benefit from non-renewal, the flatter the contract. On the other hand, when the competitor benefits from renewal of the target's debt (say non-renewal results in target's replacement by a more efficient entrant), then the optimal debt contract is nonsmooth (sometimes taking the form of a binary option), and much more profit sensitive for some profit levels than the standard contract. This increased sensitivity amplifies the competitor's incentive to price less aggressively, resulting in higher profits for the levered firm and higher payout to bondholders. In either case, our results demonstrate the optimal contract must be designed accounting for the impact of the contract itself on the profit function of the levered firm. Furthermore, bondholders prefer lending to weaker firms (firms whose competitors benefit from renewal) because the competitor's pricing incentive, amplified by the more profit sensitive contract, results in higher expected payouts.
Submitted by sirbu@math.utexas.edu
1:00p 10.176 Analysis
Alessio Figalli: Regularity results for optimal transport maps on Riemannian manifolds 1:00 pm in RLM 10.176 Analysis Seminar
Regularity results for optimal transport maps on Riemannian manifolds
Alessio Figalli (Ecole Polytechnique, Palaiseau, France )
In this talk I will describe some recent developments of the regularity theory for optimal transport maps on a Riemannian manifold when the cost function is given by the squared distance. We will see in particular that the regularity theory of optimal maps allows to study the geometry of the cut locus of the manifold.
Submitted by natasa@math.utexas.edu
Alessio Figalli: Regularity results for optimal transport maps on Riemannian manifolds 1:00 pm in RLM 10.176 Analysis Seminar
Regularity results for optimal transport maps on Riemannian manifolds
Alessio Figalli (Ecole Polytechnique, Palaiseau, France )
In this talk I will describe some recent developments of the regularity theory for optimal transport maps on a Riemannian manifold when the cost function is given by the squared distance. We will see in particular that the regularity theory of optimal maps allows to study the geometry of the cut locus of the manifold.
Submitted by natasa@math.utexas.edu
1:30p 9.166 Probability
Steven Shreve: Double Skorokhod Map and Reneging Real-Time Queues 1:30 pm in RLM 9.166 Probability
Double Skorokhod Map and Reneging Real-Time Queues
Steven Shreve (Carnegie Mellon University)
An explicit formula for the Skorokhod map on [0,a] is provided. Specifically, it is shown that on the space of right-continuous functions with left limits taking values in the real numbers,
is the unique function taking values in [0,a] that is obtained from 
by minimal "pushing'' at the endpoints 0 and a. An application of this result to real-time queues with reneging is outlined. This is joint work with L. Kruk, J. Lehoczky and K. Ramanan.
Submitted by sirbu@math.utexas.edu
Steven Shreve: Double Skorokhod Map and Reneging Real-Time Queues 1:30 pm in RLM 9.166 Probability
Double Skorokhod Map and Reneging Real-Time Queues
Steven Shreve (Carnegie Mellon University)
An explicit formula for the Skorokhod map on [0,a] is provided. Specifically, it is shown that on the space of right-continuous functions with left limits taking values in the real numbers,
is the unique function taking values in [0,a] that is obtained from by minimal "pushing'' at the endpoints 0 and a. An application of this result to real-time queues with reneging is outlined. This is joint work with L. Kruk, J. Lehoczky and K. Ramanan.
Submitted by sirbu@math.utexas.edu
2:00p ACE 6.304 ICES
Gustavo Gioia : Nikuradse meets Kolmogorov, or: How to derive the diagram from the spectrum 2:00 pm in ACE 6.304 ICES
Nikuradse meets Kolmogorov, or: How to derive the diagram from the spectrum
Gustavo Gioia (University of Illinois - Urbana)
A diagram published in 1933 remains among the weightier contributions to experimental turbulence ever. In that diagram, Nikuradse plotted six log-log curves evincing the dependence on the Reynolds number (Re) of the friction coefficient (
) of the turbulent flow in six pipes of fixed roughness. (The roughness of a pipe is the ratio 
, where 
is the size of the roughness elements that line the interior of the pipe and 
the diameter of the pipe.) Nikuradse's diagram is rich in distinctive features, including a pronounced "hump" where attains a maximum shortly after the transition to turbulence; a "smooth regime" governed by Blasius's empirical scaling, 
; shallow "bellies" where attains local minima at intermediate values of Re; and a "rough regime" governed by Strickler's empirical scaling, 
. For seventy years now, our understanding of Nikuradse's diagram has been aided by little beyond a pictorial narrative of roughness elements being progressively exposed to the turbulence as Re increases. In this seminar we identify the eddies that effect most of the momentum transfer between the viscous layer and the turbulent flow, and derive an expression for in terms of the characteristic velocity of those eddies, 
. Then we use Kolmog\'orov's spectrum for the inertial range to determine and show that the resulting expression for gives a gradual transition between the scalings of Blasius and Strickler, but fails to give the hump or the bellies of Nikuradse's diagram. To obtain an expression for that also gives the bellies, we include an exponential spectrum for the dissipation range. Last, to obtain an expression for that also gives the hump, we include von K\'arm\'an's spectrum for the energy-containing range. This final expression for is in minute qualitative agreement with Nikuradse's diagram; it affords a way of interpreting successive portions of the diagram as manifestations of the varying habits of momentum transfer; and it reveals the existence of close ties between two milestones of experimental and theoretical turbulence. This research is joint work with Pinaki Chakraborty. NOTE: I will try to explain all that is needed to understand this seminar even if you are an undergraduate student who has not been exposed to turbulence, do not be intimidated!
Submitted by gamba@math.utexas.edu
Gustavo Gioia : Nikuradse meets Kolmogorov, or: How to derive the diagram from the spectrum 2:00 pm in ACE 6.304 ICES
Nikuradse meets Kolmogorov, or: How to derive the diagram from the spectrum
Gustavo Gioia (University of Illinois - Urbana)
A diagram published in 1933 remains among the weightier contributions to experimental turbulence ever. In that diagram, Nikuradse plotted six log-log curves evincing the dependence on the Reynolds number (Re) of the friction coefficient (
) of the turbulent flow in six pipes of fixed roughness. (The roughness of a pipe is the ratio , where is the size of the roughness elements that line the interior of the pipe and the diameter of the pipe.) Nikuradse's diagram is rich in distinctive features, including a pronounced "hump" where attains a maximum shortly after the transition to turbulence; a "smooth regime" governed by Blasius's empirical scaling, ; shallow "bellies" where attains local minima at intermediate values of Re; and a "rough regime" governed by Strickler's empirical scaling, . For seventy years now, our understanding of Nikuradse's diagram has been aided by little beyond a pictorial narrative of roughness elements being progressively exposed to the turbulence as Re increases. In this seminar we identify the eddies that effect most of the momentum transfer between the viscous layer and the turbulent flow, and derive an expression for in terms of the characteristic velocity of those eddies, . Then we use Kolmog\'orov's spectrum for the inertial range to determine and show that the resulting expression for gives a gradual transition between the scalings of Blasius and Strickler, but fails to give the hump or the bellies of Nikuradse's diagram. To obtain an expression for that also gives the bellies, we include an exponential spectrum for the dissipation range. Last, to obtain an expression for that also gives the hump, we include von K\'arm\'an's spectrum for the energy-containing range. This final expression for is in minute qualitative agreement with Nikuradse's diagram; it affords a way of interpreting successive portions of the diagram as manifestations of the varying habits of momentum transfer; and it reveals the existence of close ties between two milestones of experimental and theoretical turbulence. This research is joint work with Pinaki Chakraborty. NOTE: I will try to explain all that is needed to understand this seminar even if you are an undergraduate student who has not been exposed to turbulence, do not be intimidated!
Submitted by gamba@math.utexas.edu
Conference Announcement
Future Directions in Nonlinear Partial Differential Equations
Dec 10 - 13, 2008
A meeting honoring Luis Caffarelli on the occasion of his 60th birthday
Click here for details