In early 2024, while the Northern Hemisphere sunk further into winter, a small group of math PhD students and faculty met for lectures and open discussions on mathematical neuroscience in the oceanside town of Paihia, New Zealand (on the north coast of the North Island). From January 8th to the 12th, four visiting researchers gave morning lectures on different topics in mathematical neuroscience, giving participants from a wide range of backgrounds in mathematics the chance to learn and potentially expand their future research interests. Benjamin Lindner (Bernstein Center for Computational Neuroscience and Humboldt University Berlin) covered methods in stochastic processes for neuroscience, motivating canonical stochastic models in neuroscience, and teaching key methods for analyzing model statistics. Jeff Moehlis (University of California Santa Barbara) spoke about phase models of spiking neurons with a specific focus on control, motivated by the use of deep brain stimulation to treat symptoms of Parkinson’s disease. Alla Borisyuk (University of Utah) covered diverse topics in the realm of sensory neuroscience including delay line models of sound localization, the role of synchrony in tinnitus, and how olfactory network structure shapes odor representation. Zachary Kilpatrick (University of Colorado Boulder) taught mathematical methods for the analysis of bump attractors and probabilistic descriptions of decision making by individuals in complex and social environments. Group lunches and afternoon activities afforded lecturers and participants the opportunity to connect and continue informal chats.

Figure 1. The main organizer (Carlo Laing) and four invited lecturers enjoying the view from the top of Motuarohia in the Bay of Islands. From left to right: Jeff Moehlis, Zack Kilpatrick, Carlo Laing, Benjamin Lindner, and Alla Borisyuk.

This workshop was made possible by the New Zealand Mathematics Research Institute (NZMRI), which was established in the 1990s with the aim of promoting mathematical research in New Zealand (NZ). See here for a historical note on the origins of the organization: https://www.nzmri.org/historical-notes/. NZMRI primarily organizes summer meetings on topics of contemporary significance in mathematics, featuring lectures from some of the world’s best mathematicians and allowing for interactions between invited speakers, local researchers, and graduate students. For 30 years, these workshops have been supported by various organizations and people mostly in NZ including the Marsden Fund, the NZ Institute for Mathematics and its Applications, and by individuals and university departments in NZ. Past workshops organized by NZMRI include topics in numerical methods for ODEs, stochastic processes in biology, dynamical systems (and relevant continuation methods), and random matrices. A complete list with links to past content can be found here: https://www.nzmri.org/

The NZMRI Summer Workshop on Mathematical Neuroscience was primarily organized by Carlo Laing (Massey University) with assistance from Richard Brown (Massey University). Aside from the lecturers and the main organizer, the workshop was attended by directors of the NZMRI: Astrid an Heuf (Victoria University of Wellington), Marston Conder (University of Auckland), Rod Gover (University of Auckland), Stephen Marsland (Victoria University of Wellington), Gaven Martin (Massey University). Other attendees include Bernd Krauskopf (University of Auckland), Bradley Windelborn (University of Auckland), Darius Young (University of Auckland), David Dijekma (University of Auckland), Hinke Osinga (University of Auckland), Igor Rychkov (University of Waikato), Jian Song (Massey University), Mihai Florencescu (Massey University), and Rua Murray (University of Canterbury). A program and information about the event is published at this website, and slides of all lecturers’ talks will be linked imminently: https://sites.massey.ac.nz/nzmri2024/