## Seminar Categories

- Analysis and PDE Working Seminar (4)
- Applied and Computational Math Colloquium (2)
- Automorphic Forms and Number Theory (1)
- Climate Seminar (6)
- Colloquium (2)
- Combinatorics Seminar (5)
- Commutative Algebra Seminar (5)
- IMA Data Science Lab Seminar (5)
- MCFAM Distinguished Lecture Series (1)
- MCFAM Seminar (1)
- Probability Seminar (1)

## Current Series

Mon Sep 09 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Emergent behavior in collective dynamics Eitan Tadmor, University of Maryland Collective dynamics is driven by alignment that tend to self-organize the crowd and by different external forces that keep the crowd together. Different emerging equilibria are self-organized into clusters, flocks, tissues, parties, etc. I will overview recent results on the hydrodynamics of large-time, large-crowd collective behavior, driven by different rules of engagement. In particular, I address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions. |

Mon Oct 07 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Nonuniqueness in Dynamical Systems Richard McGehee, University of Minnesota Discontinuous vector fields arise naturally in some applications. In this presentation, a simple classical model of ocean circulation is introduced as an example of how discontinuities give rise to nonunique solutions. Standard bifurcation techniques often fail when the vector field is not smooth, and certainly fail when the vector field is discontinuous. However, some topological techniques seem to carry over, and a crude birfurcation theory can be extended to a large class of discontinuous systems. |

Mon Dec 02 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Towards personalized computer simulation of breast cancer treatment Arnoldo Frigessi , University of Oslo Current personalized cancer treatment is based on biomarkers which allow assigning each patient to a subtype of the disease, for which treatment has been established. Such stratifiedpatient treatments represent a first important step away from one-size-fits-all treatment.However, the accuracy of disease classification comes short in the granularity of thepersonalization: it assigns patients to one of a few classes, within which heterogeneity inresponse to therapy usually is still very large. In addition, the combinatorial explosivequantity of combinations of cancer drugs, doses and regimens, makes clinical testingimpossible. We propose a new strategy for personalised cancer therapy, based on producing acopy of the patients tumour in a computer, and to expose this synthetic copy to multiplepotential therapies. We show how mechanistic mathematical modelling, patient specificinference and simulation can be used to predict the effect of combination therapies in a breastcancer. The model accounts for complex interactions at the cellular and molecular level, andis able of bridging multiple spatial and temporal scales. The model is a combination ofordinary and partial differential equations, cellular automata and stochastic elements. Themodel is personalised by estimating multiple parameters from individual patient data,routinely acquired, including histopathology, imaging and molecular profiling. The resultsshow that mathematical models can be personalized to predict the effect of therapies in eachspecific patient. The approach is tested with data from five breast tumours collected in arecent neoadjuvant clinical phase II trial. The model predicted correctly the outcome after 12weeks treatment and showed by simulation how alternative treatment protocols would haveproduced different, and some times better, outcomes. This study is possibly the first onetowards personalized computer simulation of breast cancer treatment incorporating relevantbiologically-specific mechanisms and multi-type individual patient data in a mechanistic andmultiscale manner: a first step towards virtual treatment comparison.Xiaoran Lai, Oliver Geier, Thomas Fleischer, Øystein Garred, Elin Borgen, Simon Funke,Surendra Kumar, Marie Rognes, Therese Seierstad, Anne-Lise Børressen-Dale, VesselaKristensen, Olav Engebråten, Alvaro Köhn-Luque, and Arnoldo Frigessi, Tow |

Mon Dec 09 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Gradient Flows: From PDE to Data Analysis Franca Hoffman, Caltech Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches. |

Mon Feb 03 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207On the final frontiers in computational mathematics Anders Hansen, Cambridge Core problems in computational mathematics include computing spectra of operators, solutions to linear PDEs, convex optimisation problems etc., and these areas have been intensely investigated over the last half century. However, there are still fundamental open problems. For example, despite more than 90 years of quantum mechanics, it is still unknown whether it is possible to compute spectra of Schrodinger operators with bounded potentials. Moreover, how to compute minimisers of linear programs (LP) with rational inputs has been known since the 1950s, however, what happens if the input is irrational? Can one accurately compute minimisers of LPs if, as in compressed sensing, the matrix has rows from the discrete cosine transform? Furthermore, do there exist algorithms that can handle all linear Schrodinger PDEs? And, if not, which can be handled and which can never be solved? We will discuss solutions to many of these open problems and provide some potentially surprising results. For example, despite being open for decades, the problem of computing spectra of Schrodinger operators with bounded potentials is not harder than computing spectra of diagonal infinite matrices, the easiest of computational spectral problems. Moreover, for LPs with irrational inputs we have the following phenomenon. For any integer K > 2 there exists a class of well conditioned inputs so that no algorithm can compute K correct digits of a minimiser, however, there exists an algorithm that can compute K-1 correct digits. But any algorithm producing K-1 correct digits will need arbitrarily long time. Finally, computing K-2 correct digits can be done in polynomial time in the number of variables. |

Mon Feb 24 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Applied and Computational Math Colloquium - Canceled Canceled |

Mon Mar 16 |
## Applied and Computational Math Colloquium3:35pm - TBAApplied and Computational Math Colloquium Mauro Maggioni, Johns Hopkins |

Mon Mar 16 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Applied and Computational Math Colloquium - Cancelled Colloquium Cancelled |

Mon Apr 13 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Applied and Computational Math Colloquium - Cancelled Dio Margetis, Maryland |

Mon May 04 |
## Applied and Computational Math Colloquium3:35pm - Vincent Hall 207Applied and Computational Math Colloquium Eric Bonnetier, Université Joseph Fourier |