The Proprietary Trading industry, a crucial cog in the financial machinery of the United States, has evolved into a complex landscape where firms leverage their capital to trade in an array of financial instruments. This discourse will delve into the industry's intricacies, shedding light on key findings and insights.

To begin with, Proprietary trading is a high-stakes venture wherein firms or banks trade stocks, bonds, currencies, commodities, their derivatives, or other financial instruments with the firm's own money, as opposed to depositors' money. The objective is to generate direct principal gains rather than earning profits through commissions by trading on behalf of clients.

The geographical distribution of Proprietary Trading firms in the US is predominantly skewed towards financial hubs such as New York and Chicago, though a considerable presence is seen in San Francisco and Boston. The geographic concentration in these cities can be attributed to their historical importance as finance and trade centers, the proximity to financial exchanges, and the aggregation of human capital in these locations.

In the temporal context, the trading industry has undergone significant transformation. The Glass-Steagall Act of 1933, which prohibited commercial banks from engaging in investment banking activities, led to the inception of prop trading firms. However, the repeal of this Act in 1999 brought commercial banks into the prop trading league. Furthermore, the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010, specifically the Volcker Rule, limited banks' ability to conduct proprietary trading. This has led to the reemergence of independent prop trading firms.

Prop trading firms employ a multitude of trading strategies. These include market making, arbitrage, statistical arbitrage, trend following, and high-frequency trading (HFT). The choice of strategy largely depends on the firm's risk appetite, the expertise of traders, and technological infrastructure. For instance, HFTs require sophisticated technology and algorithms, and are therefore typically utilized by firms with significant capital and technological prowess.

On the technology front, the advent of electronic and algorithmic trading has revolutionized the industry. The use of high-speed connections and complex algorithms enables firms to capitalize on minuscule price discrepancies and execute trades in milliseconds, thus profiting from high-volume, low-margin trades.

The industry's risk-reward proposition is contingent upon the efficient management of market risk, operational risk, and regulatory risk. Market risk pertains to potential losses from adverse market movements. Operational risk arises from potential failures in internal processes, systems, or from external events. Regulatory risk pertains to the risk of non-compliance with regulatory requirements, which could lead to fines or even loss of trading privileges.

Several notable firms exemplify successful proprietary trading. These include Jane Street, a quantitative trading firm that shines in ETF trading and Citadel Securities, a leading market maker that trades in various asset classes.

However, it is imperative to mention that proprietary trading is not without its critics. It is often seen as a high-risk activity that potentially threatens the stability of financial institutions and the broader economy. Conversely, proponents argue that prop trading provides liquidity, narrows bid-ask spreads, and aids in price discovery.

In summation, the US Prop Trading landscape is a dynamic and complex realm, characterized by high levels of risk and reward. The industry's evolution continues to be shaped by regulatory changes, technological advancements, and the economic environment. While the industry's future trajectory remains uncertain amidst increased regulatory scrutiny and market volatility, it will undoubtedly remain a pivotal component of the financial sector.