##### Department of Mathematics,

University of California San Diego

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### Optimization Seminar

## Yuan Yao

#### Peking University

## Geometric and Topological Methods for Data Analysis

##### Abstract:

Voting has been an important topic for human activities and a central theme in the social choice theory in Economics, which is featured with the celebrated Impossibility Theorems by Nobel Laureates Ken Arrow and Amartya Sen. Despite of the intrinsic conflicts between the faithful representation of individuals and the desire for consistent social orders, in reality we are still looking for possible preference aggregation rules out of impossibilities. Hodge Theory, as a bridge between the algebraic topology and geometry, is surprisingly enabling us a tool of preference aggregation as a generalization of the classical Borda count, arguably the most consistent and tractable social choice rule. It not only enables us to find aggregated preference with nearly linear complexity algorithms to deal with the rapid growth of crowdsourcing data, but also provides us ways to characterize the conflicts of interests arising locally or globally. We shall discuss these from a revisit of those impossibility theorems to see what is possible that Hodge decomposition provides us.

Host: Jiawang Nie

### February 19, 2015

### 2:00 PM

### AP&M 7218

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